Question

You are drawing one card from a shuffled deck. Let event A be "drawing a spade" and event B be "drawing a face card". You are drawing one card from a shuffled deck of 52 cards. Let event A be "drawing a spade" and event B be "drawing a face card". There are 12 face cards in a deck, of which 3 are spades. Calculate P(A | B).

Answer 1

Answer:

$\displaystyle P(A|B)=\frac{1}{4}$

Step-by-step explanation:

Conditional Probability

It's the probability that a given event A occurs, knowing another event B has occurred. It's written as P(A|B) and is calculated by the formula

$\displaystyle P(A|B)=\frac{P(A\cap B)}{P(B)}$

Let the event A=Drawing a spade and event B= Drawing a face card

Let's first compute P(B). There are 12 face cards in a deck, thus

$\displaystyle P(B)=\frac{12}{52}$

To compute $P(A\cap B)$ we use the fact that there are 3 spades out of the 12 face cards, thus

$\displaystyle P(A\cap B)=\frac{3}{52}$

Finally

$\displaystyle P(A|B)=\frac{\frac{3}{52}}{\frac{12}{52}}=\frac{3}{12}=\frac{1}{4}$

The required probability is 1/4 or 0.25