Chapter 13.10, Problem 10PPS

To determine

The probability of each card with the letters.

P (a vowel and D)

Answer to Problem 10PPS

The probability of each card with the lettersis P (a vowel and D)= $\frac{1}{28}$

Explanation of Solution

Given:Letters: $\text{A,B,C,D,E,F,G,H}$

Calculation:

Fraction Form:

The probability of getting a vowels and then a D in the fraction form is given as

P (Vowel) = $\frac{2}{8}$ or $\frac{1}{4}$

Here, $1$ means no of the vowels in the given letters and $4$ is total number of the letters.

P (D) = $\frac{1}{7}$ ,

Here $1$ is no of the $\text{D's}$ after a vowel is removed and $7$ is total number of letters after a vowel is removed.

P (a Vowel and D) = P (a Vowel) * P(D)

  $\begin{array}{l}=\frac{1}{4}\times \frac{1}{7}\\ =\left(\frac{1.1}{4.7}\right)\\ =\frac{1}{28}\end{array}$

Conclusion:

Hence, P (a vowel and D)= $\frac{1}{28}$