Chapter 12.5, Problem 2BCYP

To determine

To find the probability.

Answer to Problem 2BCYP

The probability $\text{P}\left(\text{heart, not a heart, heart}\right)=\frac{6084}{132600}\text{ or 4}\text{.6\%}$ .

Explanation of Solution

Given information:

Find the probability:

  $\text{P}\left(\text{heart, not a heart, heart}\right)$

From a deck of cards.

Formula used:

The following formula is used:

  $\text{Probability}=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$

Calculation :

The probability can be calculated by:

  $\begin{array}{l}\text{P}\left(\text{heart}\right)=\frac{13}{52}\\ \text{P}\left(\text{not a heart}\right)=\frac{39}{51}\\ \text{P}\left(\text{heart}\right)=\frac{12}{50}\\ \text{P}\left(\text{heart, not a heart, heart}\right)=\frac{13}{52}\times \frac{39}{51}\times \frac{12}{50}\\ \text{P}\left(\text{heart, not a heart, heart}\right)=\frac{6084}{132600}\text{ or 4}\text{.6\%}\end{array}$

Hence, the probability $\text{P}\left(\text{heart, not a heart, heart}\right)=\frac{6084}{132600}\text{ or 4}\text{.6\%}$ .