DP Mathematics HL Questionbank

• Syllabus

5.2

Sub sections and their related questions

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

• 12M.2.hl.TZ1.3a: In how many ways can the team be selected?
• 12M.2.hl.TZ1.3b: In how many of these selections is exactly one girl in the team?
• 12M.2.hl.TZ1.3c: If the selection of the team is made at random, find the probability that exactly one girl is in...
• 12M.1.hl.TZ2.3b: What is the probability that the “Tigers” soccer team wins?
• 12N.2.hl.TZ0.7a: Find the probability that she is successful in all three games.  
• 12N.2.hl.TZ0.7b: Assuming that she is successful in the first game, find the probability that she is successful in...
• 11M.1.hl.TZ2.9a: What is the probability that there are exactly 3 defective DVD players in the first 8 DVD players...
• 11M.1.hl.TZ2.9b: What is the probability that the \({9^{{\text{th}}}}\) DVD player examined is the...
• SPNone.1.hl.TZ0.3a: Calculate the probability that no head is obtained.
• SPNone.3sp.hl.TZ0.2a: Write down the value of \({\text{P}}(X = 1)\) and show that \({\text{P}}(X = 2) = \frac{1}{6}\).
• 10M.1.hl.TZ1.7: Two players, A and B, alternately throw a fair six-sided dice, with A starting, until one of them...
• 11M.1.hl.TZ1.1a: Find the value of \({\text{P}}(A \cup B)\) when(i)     \(A\) and \(B\) are mutually...
• 11M.1.hl.TZ1.6a: Find the probability that the rabbit tests positive for the disease.
• 14M.2.hl.TZ1.8b: Mina and Norbert each have a fair cubical die with faces labelled 1, 2, 3, 4, 5 and 6; they...
• 14M.1.hl.TZ2.11a: Mobile phone batteries are produced by two machines. Machine A produces 60% of the daily output...
• 14M.1.hl.TZ2.11b: In a pack of seven transistors, three are found to be defective. Three transistors are selected...

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

• 12M.2.hl.TZ1.3a: In how many ways can the team be selected?
• 12M.2.hl.TZ1.3b: In how many of these selections is exactly one girl in the team?
• 12M.2.hl.TZ1.3c: If the selection of the team is made at random, find the probability that exactly one girl is in...
• 12M.1.hl.TZ2.3b: What is the probability that the “Tigers” soccer team wins?
• 12M.1.hl.TZ2.11d: The domains of f and g are now restricted to {0, 1, 2, 3, 4} . By considering the values of f...
• 11M.1.hl.TZ1.1a: Find the value of \({\text{P}}(A \cup B)\) when(i)     \(A\) and \(B\) are mutually...
• 14N.2.hl.TZ0.12a: Find the probability that Ava wins on her first turn.
• 14N.2.hl.TZ0.12b: Find the probability that Barry wins on his first turn.
• 16M.2.hl.TZ1.13b.i: the total of the three numbers is 5;
• 16M.2.hl.TZ1.13b.ii: the median of the three numbers is 1.

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

• 12M.2.hl.TZ1.3a: In how many ways can the team be selected?
• 12M.2.hl.TZ1.3b: In how many of these selections is exactly one girl in the team?
• 12M.2.hl.TZ1.3c: If the selection of the team is made at random, find the probability that exactly one girl is in...
• 12M.1.hl.TZ2.3b: What is the probability that the “Tigers” soccer team wins?
• 12M.1.hl.TZ2.11d: The domains of f and g are now restricted to {0, 1, 2, 3, 4} . By considering the values of f...
• 13M.1.hl.TZ1.9: Two events A and B are such that \({\text{P}}(A \cup B) = 0.7\) and \({\text{P}}(A|B') =...
• 11M.1.hl.TZ1.1a: Find the value of \({\text{P}}(A \cup B)\) when(i)     \(A\) and \(B\) are mutually...

Use of Venn diagrams, tree diagrams, counting principles and tables of outcomes to solve problems.

• 12M.2.hl.TZ1.3a: In how many ways can the team be selected?
• 12M.2.hl.TZ1.3b: In how many of these selections is exactly one girl in the team?
• 12M.2.hl.TZ1.3c: If the selection of the team is made at random, find the probability that exactly one girl is in...
• 12M.1.hl.TZ2.3a: Draw a tree diagram to represent these events and their outcomes.
• 12M.1.hl.TZ2.3b: What is the probability that the “Tigers” soccer team wins?
• 12M.1.hl.TZ2.11d: The domains of f and g are now restricted to {0, 1, 2, 3, 4} . By considering the values of f...
• 08M.1.hl.TZ2.7: Let A and B be events such that...
• 08N.2.hl.TZ0.11Part B: There are six boys and five girls in a school tennis club. A team of two boys and two girls will...
• 13M.1.hl.TZ2.4a: Draw a tree diagram representing the possible outcomes, clearly labelling each branch with the...
• 11M.1.hl.TZ1.1a: Find the value of \({\text{P}}(A \cup B)\) when(i)     \(A\) and \(B\) are mutually...
• 09N.2.hl.TZ0.13: (a)     The first game consists of one round. If Ying obtains more heads than Mario, she receives...
• 09M.2.hl.TZ2.1: (a)     Illustrate this information on a Venn diagram. (b)     Find the probability that a...
• 09M.2.hl.TZ2.5: (a)     Find the percentage of the population that has been vaccinated. (b)     A randomly...
• 13N.2.hl.TZ0.5a: Find the probability that they watch a French movie.
• 15M.2.hl.TZ2.9a: she travels to Nashville;
• 15N.1.hl.TZ0.6a: Darren plays first, find the probability that he wins.
• 15N.1.hl.TZ0.6b: The game is now changed so that the ball chosen is replaced after each turn. Darren still plays...
• 15N.2.hl.TZ0.6: Josie has three ways of getting to school. \(30\% \) of the time she travels by car, \(20\% \) of...