Conditional Probability

If the probability of event A is 0.3 and the probability of event B given A has occurred is 0.6, what is the conditional probability of event A given B?

• 0.5

• 0.4

• 0.3

• 0.7

Answer explanation

The conditional probability of event A given B is calculated using Bayes' theorem:

P(A|B) =[ P(B|A) * P(A)] / P(B)

Substituting the given values, we get P(A|B) =( 0.6 * 0.3) / P(B)

Since P(B) = P(B|A) * P(A) + P(B|A') * P(A') =(0.6 * 0.3) + (0.6 * 0.7) = 0.6,

then P(A|B)=(0.6 * 0.3) / 0.6 = 0.3.

If the probability of rain on any given day is 0.2, what is the probability of no rain for 3 consecutive days?

• 0.6

• 0.3

• 0.512

• 0.8

Answer explanation

The probability of no rain for 3 consecutive days is calculated as (1-0.2)^3 = 0.512, hence the correct answer is 0.512.

If P(A)=0.6 and the P(B|A)=0.8, what is P(A∩B)?

• 0.2

• 0.25

• 0.75

• 0.48

Answer explanation

To find P(A∩B), use the formula P(A∩B) = P(A) * P(B|A) = 0.6 * 0.8 = 0.48. Therefore, the correct answer is 0.48.

A jar contains 10 red candies and 5 green candies. What is the probability of drawing a green candy followed by a red candy without replacement?

• 3/10

• 5/21

• 1/5

• 2/15

Answer explanation

The probability of drawing a green candy first is 5/15. After removing the green candy, there are 10 red candy out of 14 candy, then drawing a red candy is 10/14. Multiplying these probabilities gives 5/21.

Are the events "takes Spanish" and "participates in a club" independent events?

• Yes, because P(S) is the same as P(S given C).

• No, because P(S) is not the same as P(S given C).

• Yes, because P(S) is the same as P(C given S).

• No, because P(S) is not the same P(C given S).

Mathematical Equivalence

ON

• 1
• 2
• 3
• 4

Are the events "Sports" and "Community Service" independent?

• Yes, because P(S) is the same as P(S Given CS).

• No, because P(S) is not the same as P(S Given CS).

• Yes, because P(S) is the same as P(CS Given S).

• No, because P(S) is not the same as P(CS Given S).

P(J | C)

Mathematical Equivalence

ON

Let M represent the event of randomly selecting a male. Let S represent the event of randomly selecting a person that drives a SUV.

Determine if the events M and S are independent.

• Independent

• Not Independent