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Allushta [10]
3 years ago
14

Ebru has a standard deck of cards. The deck has 52 total cards and contains 4 suits: hearts, clubs, diamonds, and

Mathematics
1 answer:
Naddika [18.5K]3 years ago
3 0

Answer:

The two statements provided are correct.

- 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.

- 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.

Step-by-step explanation:

In total, there are 52 cards.

There are 4 suites; hearts, clubs, diamonds, and spades.

Meaning there are

13 hearts, 13 clubs, 13 diamonds and 13 spades.

Each suit contains cards numbered 2 – 10, a jack, a queen, a king, and an ace.

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

P(A) = n(cards that are 2s) ÷ n (total)

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

P(B) = n(spades) ÷ n(total)

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

The conditional probability, P(A|B) is given as

P(A|B) = P(A n B) ÷ P(B)

For this cards question,

P(A n B) = n(a spade that is a 2) ÷ n(total)

P(A n B) = (1/52)

So, to investigate,

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.

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

Hence, this statement is true!

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.

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

This statement is also true!

Hope this Helps!!!

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