Chapter 13.5, Problem 3CYP

To determine

Find the probability that three cards are diamond.

Answer to Problem 3CYP

  $0.0518$

Explanation of Solution

Given information:

Three cards are selected from a standard deck of $52$ cards.

  

Calculation:

Total number of cards $52$ . First card can be anything so we have $52$ choices,

  $P\left(E\right)=\frac{52}{52}$

Second card has to be the same suit as first card, so probability is, $\frac{12}{51}$

Third card has to be the same suit as first and second card, so probability is, $\frac{11}{50}$

Total probability,

  $\begin{array}{l}P\left(total\right)=\frac{52}{52}\times \frac{12}{51}\times \frac{11}{50}\\ =\frac{4C{}_3}{C{}_3}=0.0518\end{array}$