Question

A deck of playing cards has $52$ cards, of which $12$ are face cards. If you shuffle the deck well and turn over the top $3$ cards, one after the other, what’s the probability that all 3 are face cards?$\left(a\right)0.001\left(b\right)0.005\left(c\right)0.010\left(d\right)0.012\left(e\right)0.02$

Short answer

The correct option is $\left(c\right)0.010$

Step-by-step solution

Step 1. Given

The number of face cards in the deck is $12$

A deck of $52$ cards has $52$ cards in it.

Step 2. Concept

Total number of cards in a deck is $52$

Step 3. Calculation

The likelihood of all three cards being face cards is computed as follows:

$P(3facecards)=\frac{12}{52}\times \frac{11}{51}\times \frac{10}{50}=\frac{1320}{132600}=0.010$

As a result, $0.010$ is the required probability.

As a result, the correct option is (c).