Question

The probability of drawing two clubs from a standard 52 card deck is 0.0588. The probability of drawing the first club is 0.25. What is the probability of drawing a second club, given the first card drawn was a club?

Answer 1

The probability of drawing a second club is 0.235

Explanation:

Given:

Probability of drawing two clubs from a standard 52 card deck = 0.0588.

Probability of drawing the first club = 0.25

To Find:

The probability of drawing a second club = ?

Solution:

Method 1:

After taking the first club from the total 13 club cards we will have 12 club remaining

Similarly the total number of cards in the deck will also be 51.

Thus the probability of taking the second club card from the deck will be =>
`(12)/(51)`

=>0.235

Method 2:

Let

P(A) be the probability of drawing the first card

P(B) be the probability of drawing the second card

P(A) and P(B) are independent event, so

`P( A \text{ and } B) = P(A) \cdot P(B)`

`0.0588 = (0.25) \cdot P(B)`

`P(B) = (0.0588)/(0.25)`

`P(B) =0.235`