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Independent events and conditional probability - MYP Questionbank | RevisionDojo

Practice Independent events and conditional probability with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

A weather station predicts rain with probability $0.3$ . If it rains, the probability that a tennis match is cancelled is $0.8$ . If it does not rain, the probability that the match is cancelled is $0.1$ . Given that the match was cancelled, what is the probability that it rained?

Question 2

In a local survey, $60\%$ of participants like coffee ( $C$ ), $40\%$ like tea ( $T$ ), and $20\%$ like neither. Find $P(C \mid T)$ .

Question 3

A train is late with probability $\frac{1}{4}$ (misses appointment with probability $\frac{3}{5}$ ) and is on time with probability $\frac{3}{4}$ (misses appointment with probability $\frac{1}{5}$ ). Calculate the total probability that Minnie misses her dentist appointment.

Question 4

In a group of 80 students, 50 play football ( $F$ ), 30 play cricket ( $C$ ), and 10 play both. A student is chosen at random from those who play football. Find the probability that they also play cricket.

Question 5

Given two events $A$ and $B$ such that $A \subseteq B$ and $\text{P}(A) > 0$ , determine the value of $\text{P}(B \mid A)$ .

Question 6

A train is late with probability $\frac{1}{4}$ . If it is late, Minnie misses her appointment with probability $\frac{3}{5}$ . If it is not late, she misses with probability $\frac{1}{5}$ . Calculate the probability that the train is NOT late and Minnie does NOT miss her appointment.

Question 7

In a Venn diagram of 30 items, event $A$ contains 10 items, event $B$ contains 15 items, and the intersection $A \cap B$ contains 5 items. Calculate $P(A \mid B)$ .

Question 8

In a multi-stage experiment, $P(A) = 0.6$ . The conditional probabilities are $P(B \mid A) = 0.3$ and $P(B \mid A') = k$ . If the total probability $P(B) = 0.4$ , find the value of $k$ .

Question 9

Given two events $A$ and $B$ such that $P(A) = x$ , $P(B) = 0.2$ , and $P(A \cup B) = 0.6$ . If $A$ and $B$ are independent, find the value of $x$ .

Question 10

Two events $A$ and $B$ are such that $P(A) = 0.5$ , $P(B) = 0.5$ , and the probability that neither $A$ nor $B$ occurs is $0.25$ .

Which of the following statements about events $A$ and $B$ is correct?

Type

Difficulty

Question 1

Question 2

In a local survey, $60\%$ of participants like coffee ( $C$ ), $40\%$ like tea ( $T$ ), and $20\%$ like neither. Find $P(C \mid T)$ .

Question 3

Question 4

Question 5

Given two events $A$ and $B$ such that $A \subseteq B$ and $\text{P}(A) > 0$ , determine the value of $\text{P}(B \mid A)$ .

Question 6

Question 7

In a Venn diagram of 30 items, event $A$ contains 10 items, event $B$ contains 15 items, and the intersection $A \cap B$ contains 5 items. Calculate $P(A \mid B)$ .

Question 8

In a multi-stage experiment, $P(A) = 0.6$ . The conditional probabilities are $P(B \mid A) = 0.3$ and $P(B \mid A') = k$ . If the total probability $P(B) = 0.4$ , find the value of $k$ .

Question 9

Given two events $A$ and $B$ such that $P(A) = x$ , $P(B) = 0.2$ , and $P(A \cup B) = 0.6$ . If $A$ and $B$ are independent, find the value of $x$ .

Question 10

Two events $A$ and $B$ are such that $P(A) = 0.5$ , $P(B) = 0.5$ , and the probability that neither $A$ nor $B$ occurs is $0.25$ .

Which of the following statements about events $A$ and $B$ is correct?

Type

Difficulty

Question 1

Question 2

In a local survey, $60\%$ of participants like coffee ( $C$ ), $40\%$ like tea ( $T$ ), and $20\%$ like neither. Find $P(C \mid T)$ .

Question 3

Question 4

Question 5

Given two events $A$ and $B$ such that $A \subseteq B$ and $\text{P}(A) > 0$ , determine the value of $\text{P}(B \mid A)$ .

Question 6

Question 7

In a Venn diagram of 30 items, event $A$ contains 10 items, event $B$ contains 15 items, and the intersection $A \cap B$ contains 5 items. Calculate $P(A \mid B)$ .

Question 8

In a multi-stage experiment, $P(A) = 0.6$ . The conditional probabilities are $P(B \mid A) = 0.3$ and $P(B \mid A') = k$ . If the total probability $P(B) = 0.4$ , find the value of $k$ .

Question 9

Given two events $A$ and $B$ such that $P(A) = x$ , $P(B) = 0.2$ , and $P(A \cup B) = 0.6$ . If $A$ and $B$ are independent, find the value of $x$ .

Question 10

Two events $A$ and $B$ are such that $P(A) = 0.5$ , $P(B) = 0.5$ , and the probability that neither $A$ nor $B$ occurs is $0.25$ .

Which of the following statements about events $A$ and $B$ is correct?

Independent events and conditional probability Questionbank