Question

Sherry has a standard deck of cards. The deck has 52 total cards and contains 4 suits: hearts, clubs, diamonds, and spades. Each suit contains cards numbered 2 - 10, a jack, a queen, a king, and an ace.

Sherry randomly selects a card. Let A be the event that the card is a king and B be the event that it is a 3.
Which of the following statements are true?
Choose all answers that apply:
P(A | B ) = P(A), the conditional probability that Sherry selects a king given that she has chosen a 3 is equal to the probability that Sherry selects a king.
P(B | A ) = P(B), the conditional probability that Sherry selects a 3 given that she has chosen a king is equal to the probability that Sherry selects a 3.
Events A and B are independent events.
The outcomes of events A and B are dependent on each other.
P(A and B)=P(A)•P(B)

Answer 1

c) Events A and B are independent events.

The outcomes of events A and B are dependent on each other.

P(A and B)=P(A)•P(B)

Explanation:

Given:

Total number, n = 52

Each suit contains 13 cards: 2 to 10, a jack, a queen, a king, and an ace.

Since there are 4 suits, it means the number of each card is four.

P(A) = event of picking a king

P(B) = event of picking a 3

Therefore the probability of picking a king =
`P(A) = (4)/(52)`

Probability of picking a 3 =
`P(B) = (4)/(52)`

Since only a card is picked, the probability a king is picked after picking a 3 is 0.

i.e P(A|B) = 0 ≠
`P(A) = (4)/(52)`

option A is wrong

The probability a 3 is picked after picking a king is 0.

i.e P(B | A) = 0 ≠
`P(B) = (4)/(52)`

option B is wrong

Events A and B are independent events.

The outcomes of events A and B are dependent on each other.

P(A and B)=P(A)•P(B)

Option C is correct.