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Ebru 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.
Ebru randomly selects a card. Let A be the event that the card is a 2 and B be the event that it is a spade. Which of the following statements are true? Choose all that apply.

a.) P(A | B)=P(A) the conditional probability that Ebru selects a 2 given that she has chosen a spade is equal to the probability that Ebru selects a 2

b.) P(B | A)=P(B) the conditional probability that Ebru selects a spade given that she has chosen a 2 is equal to the probability that Ebru selects a spade.

c.) Events A and B are independent events.

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

e.) P(A and B)=P(A)⋅P(B) the probability that Ebru selects a card that is a 2 and a spade is equal to the probability that Ebru selects a 2 multiplied by the probability that she selects a spade.

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akiran007

Answer:

None of these

Step-by-step explanation:

Let A be the event that the card is a 2 and B be the event that it is a spade.

There are 4 occurrences of 2 in a deck of 52 cards and similarly there are 13 occurrences of spade in a deck of 52 cards.

Now P(A) = 4/52

Given that event A has occurred there remains 1 occurrence that would be a spade i.e. P(B/A)= 1/13

Now we need to calculate the probability of joint event AП B  by the rule.

P( AП B) = P(A). P(B/A)

= (4/52)* (1/13)= 0.0769* 0.0769= 0.0059=0.006

Answer: A: P(A | B)=P(A) B: P(B | A)=P(B) E: P(A and B)=P(A)⋅P(B)

Step-by-step explanation:

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