DP Mathematics SL Questionbank

• Syllabus

5.7

Sub sections and their related questions

Concept of discrete random variables and their probability distributions.

• 12N.1.sl.TZ0.1a: Find AB .
• 12N.1.sl.TZ0.1b: Given that \({\boldsymbol{X}} - 2{\boldsymbol{A}} = {\boldsymbol{B}}\), find X.
• 12N.1.sl.TZ0.2a: Find the value of k .
• 12N.1.sl.TZ0.2b: Find \({\text{E}}(X)\) .
• 12M.1.sl.TZ2.4a: Find the value of r .
• 12M.1.sl.TZ2.4b: Given that \({\rm{E}}(X) = 1.4\) , find the value of p and of q .
• 08M.2.sl.TZ2.4a: Find the value of k.
• 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...
• 10N.2.sl.TZ0.9a(i) and (ii): (i)     Find E(X ) . (ii)    Find the probability that Mark passes the test.
• 10N.2.sl.TZ0.9b(i) and (ii): (i)     Show that \(4a + 2b = 0.24\) . (ii)    Given that \({\rm{E}}(Y) = 1\) , find a and b .
• 10N.2.sl.TZ0.9c: Find which student is more likely to pass the test.
• 11N.1.sl.TZ0.5: The random variable X has the following probability distribution. Given that...
• 11M.1.sl.TZ1.4a: Write down \({\rm{P}}(X = 2)\) .
• 11M.1.sl.TZ1.4b: Show that \(k = 3\) .
• 11M.1.sl.TZ1.4c: Find \({\rm{E}}(X)\) .
• 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...
• 13M.1.sl.TZ1.9b: Find the expected number of green marbles drawn from the jar.
• 13M.2.sl.TZ2.9a: (i)     Find \({\rm{P}}(X = 0)\) . (ii)     Find \({\rm{P}}(X = 1)\) . (iii)    Hence, find...
• 08M.1.sl.TZ1.10d: (i)     Construct a probability distribution table for X. (ii)    Calculate the expected value...
• 14N.1.sl.TZ0.3a: Find the probability that the dart does not hit the board.
• 14N.1.sl.TZ0.3b: The contestant scores points as shown in the following table. Given that the game is fair,...
• 15M.1.sl.TZ1.1a: Find \(p\).
• 15N.2.sl.TZ0.2a: Find the value of \(k\).
• 16M.2.sl.TZ1.8a: Find \(k\).
• 16M.2.sl.TZ1.8b: (i)     A day is chosen at random. Write down the probability that Machine A has no...
• 16N.2.sl.TZ0.7a: Write down the probability that the first disc selected is red.
• 16N.2.sl.TZ0.7b: Let \(X\) be the number of red discs selected. Find the smallest value of \(m\) for which...
• 17M.1.sl.TZ1.10a: Show that \(\cos \theta  = \frac{3}{4}\).
• 17M.1.sl.TZ1.10b: Given that \(\tan \theta  > 0\), find \(\tan \theta \).
• 17M.1.sl.TZ1.10c: Let \(y = \frac{1}{{\cos x}}\), for \(0 < x < \frac{\pi }{2}\). The graph of \(y\)between...
• 17N.2.sl.TZ0.4a: Find the value of \(k\).
• 17N.2.sl.TZ0.4b: Write down \({\text{P}}(X = 2)\).
• 17N.2.sl.TZ0.4c: Find \({\text{P}}(X = 2|X > 0)\).
• 18M.2.sl.TZ1.2a: Find the value of k.
• 18M.2.sl.TZ1.2b: Calculate the expected value of the score.
• 18M.2.sl.TZ1.2c: The die is rolled 80 times. On how many rolls would you expect to obtain a three?
• 18M.2.sl.TZ2.10a.i: Write down the value of k.
• 18M.2.sl.TZ2.10a.ii: Show that μ = 106.
• 18M.2.sl.TZ2.10b: Find P(M < 95) .
• 18M.2.sl.TZ2.10d.i: Find the expected number of bags in this crate that contain at most one small apple.
• 18M.2.sl.TZ2.10d.ii: Find the probability that at least 48 bags in this crate contain at most one small apple.

Expected value (mean), \({\text{E}}(X)\) for discrete data.

• 12N.1.sl.TZ0.1a: Find AB .
• 12N.1.sl.TZ0.1b: Given that \({\boldsymbol{X}} - 2{\boldsymbol{A}} = {\boldsymbol{B}}\), find X.
• 12N.1.sl.TZ0.2b: Find \({\text{E}}(X)\) .
• 12M.1.sl.TZ2.4a: Find the value of r .
• 12M.1.sl.TZ2.4b: Given that \({\rm{E}}(X) = 1.4\) , find the value of p and of q .
• 08M.2.sl.TZ2.4b: Find the expected value of X.
• 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.2.sl.TZ1.8e: Find \({\text{E}}(X)\) .
• 09M.1.sl.TZ2.9c: Find the expected value of S.
• 10N.2.sl.TZ0.9a(i) and (ii): (i)     Find E(X ) . (ii)    Find the probability that Mark passes the test.
• 10N.2.sl.TZ0.9b(i) and (ii): (i)     Show that \(4a + 2b = 0.24\) . (ii)    Given that \({\rm{E}}(Y) = 1\) , find a and b .
• 10N.2.sl.TZ0.9c: Find which student is more likely to pass the test.
• SPNone.1.sl.TZ0.9b: Elena plays a game where she tosses two dice. If the sum is 6, she wins 3 points. If the sum is...
• 11N.1.sl.TZ0.5: The random variable X has the following probability distribution. Given that...
• 11M.1.sl.TZ1.4a: Write down \({\rm{P}}(X = 2)\) .
• 11M.1.sl.TZ1.4b: Show that \(k = 3\) .
• 11M.1.sl.TZ1.4c: Find \({\rm{E}}(X)\) .
• 13M.1.sl.TZ1.9b: Find the expected number of green marbles drawn from the jar.
• 08M.1.sl.TZ1.10d: (i)     Construct a probability distribution table for X. (ii)    Calculate the expected value...
• 14N.1.sl.TZ0.3b: The contestant scores points as shown in the following table. Given that the game is fair,...
• 15M.1.sl.TZ1.1b: Find \({\text{E}}(X)\).
• 15N.2.sl.TZ0.2b: Find \({\text{E}}(X)\).
• 16M.2.sl.TZ1.8a: Find \(k\).
• 16M.2.sl.TZ1.8b: (i)     A day is chosen at random. Write down the probability that Machine A has no...
• 17M.2.sl.TZ1.4a: Find \(k\).
• 17M.2.sl.TZ1.4b.i: Hence, find the probability that exactly \(k\) students are left handed;
• 17M.2.sl.TZ1.4b.ii: Hence, find the probability that fewer than \(k\) students are left handed.
• 18M.2.sl.TZ1.2a: Find the value of k.
• 18M.2.sl.TZ1.2b: Calculate the expected value of the score.
• 18M.2.sl.TZ1.2c: The die is rolled 80 times. On how many rolls would you expect to obtain a three?

Applications.

• 09M.1.sl.TZ2.9d: Anna plays a game where she wins \(\$ 50\) if S is even and loses \(\$ 30\) if S is odd. Anna...
• SPNone.1.sl.TZ0.9b: Elena plays a game where she tosses two dice. If the sum is 6, she wins 3 points. If the sum is...
• 13M.1.sl.TZ1.9b: Find the expected number of green marbles drawn from the jar.
• 14N.1.sl.TZ0.3a: Find the probability that the dart does not hit the board.
• 14N.1.sl.TZ0.3b: The contestant scores points as shown in the following table. Given that the game is fair,...
• 16M.2.sl.TZ1.8a: Find \(k\).
• 16M.2.sl.TZ1.8b: (i)     A day is chosen at random. Write down the probability that Machine A has no...
• 17M.2.sl.TZ1.4a: Find \(k\).
• 17M.2.sl.TZ1.4b.i: Hence, find the probability that exactly \(k\) students are left handed;
• 17M.2.sl.TZ1.4b.ii: Hence, find the probability that fewer than \(k\) students are left handed.
• 18M.2.sl.TZ1.2a: Find the value of k.
• 18M.2.sl.TZ1.2b: Calculate the expected value of the score.
• 18M.2.sl.TZ1.2c: The die is rolled 80 times. On how many rolls would you expect to obtain a three?