DP Mathematics SL Questionbank

• Syllabus

5.5

Sub sections and their related questions

Concepts of trial, outcome, equally likely outcomes, sample space ( \(U\) ) and event.

• 11M.2.sl.TZ2.9a: List the pairs of scores that give a sum of 6.
• 11M.2.sl.TZ2.9b: The probability distribution for the sum of the scores on the two dice is shown below. Find...
• 11M.2.sl.TZ2.9c: Fred plays a game. He throws two fair 4-sided dice four times. He wins a prize if the sum is 5 on...
• 16M.1.sl.TZ2.8a: (i)     Write down the value of \(p\). (ii)     Find the value of \(q\). (iii)     Write down...
• 18M.2.sl.TZ1.5a: Find P(A ∩ B′ ).
• 18M.2.sl.TZ1.5b: Given that P((A ∪ B)′ ) = 0.19, find P(A | B′ ).
• 18M.1.sl.TZ2.8a: Copy and complete the following tree diagram.
• 18M.1.sl.TZ2.8b: Find the probability that Pablo leaves home before 07:00 and is late for work.
• 18M.1.sl.TZ2.8c: Find the probability that Pablo is late for work.
• 18M.1.sl.TZ2.8d: Given that Pablo is late for work, find the probability that he left home before 07:00.
• 18M.1.sl.TZ2.8e: Two days next week Pablo will drive to work. Find the probability that he will be late at least...

The probability of an event \(A\) is \(P\left( A \right) = \frac{{n\left( A \right)}}{{n\left( U \right)}}\) .

• 12M.2.sl.TZ1.8a(i) and (ii): (i)     Write down the value of p and of q . (ii)    Write down the median class.
• 12M.2.sl.TZ1.8b: A child is selected at random. Find the probability that the child takes less than 95 seconds to...
• 12M.2.sl.TZ1.8c(i) and (ii): Consider the class interval \(45 \le T < 55\) . (i)     Write down the interval...
• 12M.2.sl.TZ1.8e: John assumes that T is normally distributed and uses this to estimate the probability that a...
• 09N.1.sl.TZ0.8b: One boy is selected at random. (i)     Find the probability that he plays only one...
• 09M.1.sl.TZ1.2a: Find \({\rm{P}}(A)\) .
• 09M.2.sl.TZ1.8c: In order to sell the fish, the fisherman classifies them as small, medium or large. Small fish...
• 09M.1.sl.TZ2.9b: Let S be the sum of the numbers on the two cards. Find the probability of each value of S.
• SPNone.1.sl.TZ0.9a(i), (ii) and (iii): (i)     Find \({\rm{P}}(X = 6)\) . (ii)    Find \({\rm{P}}(X > 6)\) . (iii)   Find...
• 11N.1.sl.TZ0.3a: Write down the probability that the first marble Anna selects is red.
• 11N.1.sl.TZ0.3b: Find the probability that Anna selects two red marbles.
• 11N.1.sl.TZ0.3c: Find the probability that one marble is red and one marble is blue.
• 11N.1.sl.TZ0.7a: Find the values of k such that \(f(x) = 0\) has two equal roots.
• 11N.1.sl.TZ0.7b: Each value of k is equally likely for \( - 5 \le k \le 5\) . Find the probability that...
• 11N.2.sl.TZ0.2a: Write down the median value.
• 11N.2.sl.TZ0.2b: A boy is chosen at random. Find the probability that he is shorter than \(161{\text{ cm}}\).
• 11N.2.sl.TZ0.2c: Given that \(82\% \) of the boys are taller than \(h{\text{ cm}}\), find h .
• 11M.1.sl.TZ1.8a(i), (ii) and (iii): (i)     Write down the value of s . (ii)    Find the value of q . (iii)   Write down the value...
• 11M.1.sl.TZ1.8b(i) and (ii): (i)     A student is selected at random. Given that the student takes music, write down the...
• 11M.1.sl.TZ1.8c: Two students are selected at random, one after the other. Find the probability that the first...
• 13M.1.sl.TZ1.9a: Find the probability that   (i)     none of the marbles are green;   (ii)     exactly one...
• 13M.2.sl.TZ1.10e: In one rotation of the wheel, find the probability that a randomly selected seat is at least...
• 13M.1.sl.TZ2.8b: A girl is chosen at random.   (i)     Find the probability that the time she takes is less than...
• 13M.2.sl.TZ2.9a: (i)     Find \({\rm{P}}(X = 0)\) . (ii)     Find \({\rm{P}}(X = 1)\) . (iii)    Hence, find...
• 08M.1.sl.TZ1.10a: Write down (i)     P(B);(ii)    P(R).
• 14N.2.sl.TZ0.8d: A family is chosen at random. (i)     Find the probability that this family lives in an...
• 15M.1.sl.TZ1.10a: Find the probability that Ann wins on her first roll.
• 16M.1.sl.TZ2.8a: (i)     Write down the value of \(p\). (ii)     Find the value of \(q\). (iii)     Write down...
• 17N.1.sl.TZ0.1a: Complete the following tree diagram.
• 17N.1.sl.TZ0.1b: Find the probability that exactly one of the selected balls is green.
• 18M.2.sl.TZ1.5a: Find P(A ∩ B′ ).
• 18M.2.sl.TZ1.5b: Given that P((A ∪ B)′ ) = 0.19, find P(A | B′ ).
• 18M.1.sl.TZ2.8a: Copy and complete the following tree diagram.
• 18M.1.sl.TZ2.8b: Find the probability that Pablo leaves home before 07:00 and is late for work.
• 18M.1.sl.TZ2.8c: Find the probability that Pablo is late for work.
• 18M.1.sl.TZ2.8d: Given that Pablo is late for work, find the probability that he left home before 07:00.
• 18M.1.sl.TZ2.8e: Two days next week Pablo will drive to work. Find the probability that he will be late at least...

The complementary events \(A\) and \({A'}\) (not \(A\)).

• 12M.1.sl.TZ1.4a: Write down the value of t .
• 12M.1.sl.TZ1.4b(i) and (ii): (i)     Show that \(r = 0.2\) . (ii)    Write down the value of q and of s .
• 12M.1.sl.TZ1.4c(i) and (ii): (i)     Write down \({\rm{P}}(B')\) . (ii)    Find \({\rm{P}}(A|B')\) .
• 12M.2.sl.TZ1.8d(i) and (ii): Hence find an estimate for the (i)     mean; (ii)    standard deviation.
• 10N.1.sl.TZ0.4a: Write down the value of p .
• 10N.1.sl.TZ0.4b: Find \({\rm{P}}(B)\) .
• 10N.1.sl.TZ0.4c: Find \({\rm{P}}(A'|B)\) .
• 10M.1.sl.TZ1.5a(i), (ii) and (iii): Write down the value of (i)     p ; (ii)    q ; (iii)   r.
• 10M.1.sl.TZ1.5b: Find the value of \({\rm{P}}(A|B')\) .
• 10M.1.sl.TZ1.5c: Hence, or otherwise, show that the events A and B are not independent.
• 09M.2.sl.TZ1.8d: The cost of a small fish is \(\$ 4\), a medium fish \(\$ 10\), and a large fish \(\$ 12\). Copy...
• 11M.2.sl.TZ1.7a: Find the probability that it passes inspection.
• 11M.2.sl.TZ1.7b: The company would like the probability that a box passes inspection to be 0.87. Find the...
• 11M.1.sl.TZ2.2a(i) and (ii): (i)     Write down the value of n . (ii)    Find the value of m , of p , and of q .
• 11M.1.sl.TZ2.2b: Find \({\rm{P}}(B')\) .
• 14M.1.sl.TZ1.5: Celeste wishes to hire a taxicab from a company which has a large number of taxicabs. The...
• 14M.1.sl.TZ1.9a: Copy and complete the following tree diagram. (Do not write on this page.)  
• 14M.1.sl.TZ1.9c: Find the probability that Bill wins at least one game.
• 13N.2.sl.TZ0.10d: After \(n\) school days, the probability that Samantha goes to school by bus at least once is...
• 14N.1.sl.TZ0.8a: Find the value of \(p\).
• 15N.2.sl.TZ0.5c: Find \({\text{P}}(C'|D)\).
• 16M.1.sl.TZ2.8a: (i)     Write down the value of \(p\). (ii)     Find the value of \(q\). (iii)     Write down...
• 17N.1.sl.TZ0.1a: Complete the following tree diagram.
• 17N.1.sl.TZ0.1b: Find the probability that exactly one of the selected balls is green.
• 18M.2.sl.TZ1.5a: Find P(A ∩ B′ ).
• 18M.2.sl.TZ1.5b: Given that P((A ∪ B)′ ) = 0.19, find P(A | B′ ).
• 18M.1.sl.TZ2.8a: Copy and complete the following tree diagram.
• 18M.1.sl.TZ2.8b: Find the probability that Pablo leaves home before 07:00 and is late for work.
• 18M.1.sl.TZ2.8c: Find the probability that Pablo is late for work.
• 18M.1.sl.TZ2.8d: Given that Pablo is late for work, find the probability that he left home before 07:00.
• 18M.1.sl.TZ2.8e: Two days next week Pablo will drive to work. Find the probability that he will be late at least...

Use of Venn diagrams, tree diagrams and tables of outcomes.

• 12M.1.sl.TZ2.9a(i) and (ii): Bag A contains three white balls and four red balls. Two balls are chosen at random without...
• 12M.1.sl.TZ2.9b: Bag A contains three white balls and four red balls. Two balls are chosen at random without...
• 12M.1.sl.TZ2.9c: Bag A contains three white balls and four red balls. Two balls are chosen at random without...
• 12M.1.sl.TZ1.4a: Write down the value of t .
• 12M.1.sl.TZ1.4b(i) and (ii): (i)     Show that \(r = 0.2\) . (ii)    Write down the value of q and of s .
• 12M.1.sl.TZ1.4c(i) and (ii): (i)     Write down \({\rm{P}}(B')\) . (ii)    Find \({\rm{P}}(A|B')\) .
• 10N.1.sl.TZ0.4a: Write down the value of p .
• 10N.1.sl.TZ0.4b: Find \({\rm{P}}(B)\) .
• 10N.1.sl.TZ0.4c: Find \({\rm{P}}(A'|B)\) .
• 10M.1.sl.TZ1.5a(i), (ii) and (iii): Write down the value of (i)     p ; (ii)    q ; (iii)   r.
• 10M.1.sl.TZ1.5b: Find the value of \({\rm{P}}(A|B')\) .
• 10M.1.sl.TZ1.5c: Hence, or otherwise, show that the events A and B are not independent.
• 10M.1.sl.TZ2.9a(i) and (ii): Find (i)     \({\rm{P}}(E \cap F)\) ; (ii)    \({\rm{P}}(F)\) .
• 10M.1.sl.TZ2.9b(i) and (ii): Find the probability that (i)     José misses his bus and is not late for school; (ii)    José...
• 10M.1.sl.TZ2.9c: The cost for each day that José catches the bus is 3 euros. José goes to school on Monday and...
• 10M.1.sl.TZ2.9d: The cost for each day that José catches the bus is 3 euros. José goes to school on Monday and...
• 09M.1.sl.TZ2.9a: Copy and complete the table below to show all nine equally likely outcomes.
• 11M.1.sl.TZ1.8a(i), (ii) and (iii): (i)     Write down the value of s . (ii)    Find the value of q . (iii)   Write down the value...
• 11M.1.sl.TZ1.8b(i) and (ii): (i)     A student is selected at random. Given that the student takes music, write down the...
• 11M.1.sl.TZ1.8c: Two students are selected at random, one after the other. Find the probability that the first...
• 11M.1.sl.TZ2.2a(i) and (ii): (i)     Write down the value of n . (ii)    Find the value of m , of p , and of q .
• 11M.1.sl.TZ2.2b: Find \({\rm{P}}(B')\) .
• 14M.1.sl.TZ1.9a: Copy and complete the following tree diagram. (Do not write on this page.)  
• 14M.2.sl.TZ2.4c(i): On the following Venn diagram, shade the region that represents \(A \cap B'\).
• 14M.2.sl.TZ2.4c(ii): Find \({\text{P}}(A \cap B')\).
• 14N.1.sl.TZ0.8a: Find the value of \(p\).
• 15M.1.sl.TZ1.10a: Find the probability that Ann wins on her first roll.
• 16M.1.sl.TZ2.8a: (i)     Write down the value of \(p\). (ii)     Find the value of \(q\). (iii)     Write down...
• 17M.1.sl.TZ1.1a.i: Find the value of \(p\);
• 17M.1.sl.TZ1.1a.ii: Find the value of \(q\).
• 17M.1.sl.TZ1.1b: A girl is selected at random. Find the probability that she takes economics but not history.
• 17N.1.sl.TZ0.1a: Complete the following tree diagram.
• 17N.1.sl.TZ0.1b: Find the probability that exactly one of the selected balls is green.
• 18M.2.sl.TZ1.5a: Find P(A ∩ B′ ).
• 18M.2.sl.TZ1.5b: Given that P((A ∪ B)′ ) = 0.19, find P(A | B′ ).
• 18M.1.sl.TZ2.8a: Copy and complete the following tree diagram.
• 18M.1.sl.TZ2.8b: Find the probability that Pablo leaves home before 07:00 and is late for work.
• 18M.1.sl.TZ2.8c: Find the probability that Pablo is late for work.
• 18M.1.sl.TZ2.8d: Given that Pablo is late for work, find the probability that he left home before 07:00.
• 18M.1.sl.TZ2.8e: Two days next week Pablo will drive to work. Find the probability that he will be late at least...