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You have a standard deck of cards. The deck has 52 total cards and contains 4 suits: hearts, clubs, diamonds, and spades. Each suit consists of cards numbered 2-10, a jack, a queen, a king, and an ace.
You select one card at random from the deck. Let A be the event that the randomly selected card is a diamond and let B be the event that the card is a king. Based on this information, answer the following questions.

1)What is P(A|B), the conditional probability that the card is a diamond given that it is a king?

2)Are the events A and B independent?

Respuesta :

amna04352

Answer:

1) ¼

2) yes

Step-by-step explanation:

1) P(A) = 13/52 = 1/4

P(B) = 4/52 = 1/13

P(A^B) = 1/52

P(A|B) = (1/52) ÷ (1/13) = 1/4

Since P(A|B) = P(A), they are independent

The conditional probability that the card is a diamond given that it is a king is 1/4 and the events are independent.

What is probability?

It is defined as the ratio of the number of favorable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

It is given that:

The deck has 52 total cards and contains 4 suits: hearts, clubs, diamonds, and spades.

Each suit consists of cards numbered 2-10, a jack, a queen, a king, and an ace.

Total number of cards = 52

Or

Total number of outcomes = 52

Total number of favorable outcomes = 13

The probability of event A:

P(A) = 13/52 = 1/4

The probability of event B:

P(B) = 4/52 = 1/13

P(A^B) = P(A)P(B)=  1/52

P(A|B) = (1/52)/(1/13) = 1/4

Since P(A|B) = P(A), they are independent

Thus, the conditional probability that the card is a diamond given that it is a king is 1/4 and the events are independent.

Learn more about the probability here:

brainly.com/question/11234923

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