Probability Concepts for Grade 12

What is the conditional probability of event A given event B if P(A) = 0.4 and P(B) = 0.5, and P(A ∩ B) = 0.2?

• 0.2

• 0.4

• 0.5

• 0.1

If two events A and B are independent, what is P(A ∩ B) if P(A) = 0.3 and P(B) = 0.6?

• 0.12

• 0.9

• 0.36

• 0.18

Calculate the conditional probability P(A | B) if P(A) = 0.5, P(B) = 0.4, and P(A ∩ B) = 0.2.

• 0.3

• 0.8

• 0.5

• 0.1

Determine if the events A and B are independent if P(A) = 0.5, P(B) = 0.3, and P(A ∩ B) = 0.15.

• A and B are independent only if P(A ∩ B) = 0.2.

• P(A ∩ B) must equal P(A) + P(B) for independence.

• No, A and B are dependent.

• Yes, A and B are independent.

If P(A) = 0.7 and P(B) = 0.2, what is P(A ∪ B) assuming A and B are independent?

• 0.76

• 0.3

• 0.9

• 0.5

What is the probability of event A occurring if P(A | B) = 0.6, P(B) = 0.5, and P(A ∩ B) = 0.3?

• 0.5

• 0.8

• 0.3

• 0.6

If P(A) = 0.4 and P(B) = 0.5, what is P(A ∩ B) if A and B are independent?

• 0.1

• 0.6

• 0.2

• 0.3

Calculate P(A | B) if P(A) = 0.8, P(B) = 0.6, and P(A ∩ B) = 0.48.

• 0.48

• 0.8

• 0.5

• 0.6

Two events A and B are such that P(A) = 0.5 and P(B) = 0.5. If they are independent, what is P(A ∪ B)?

• 0.5

• 1.0

• 0.25

• 0.75

If P(A) = 0.3 and P(B) = 0.4, what is P(A ∩ B) if A and B are not independent?

• P(A ∩ B) = 0.1

• Cannot be determined without additional information.

• P(A ∩ B) = 0.12

• P(A ∩ B) = 0.7