Chapter 10.2, Problem 14E

To determine

To calculate:

The probability value of first tile of consonant and second tile of vowel

Answer to Problem 14E

The probability value of first tile of consonant and second tile of vowel is $0.2375$ .

Explanation of Solution

Given information:

  

Event $A$ : Selection of the first tile of consonant

Event $B$ : Selection of the second tile of vowel

Calculation:

From the given figure:

Vowels: $A+E+I+O+U=9+12+9+8+4=42$

Blanks: $2$

Consonants: $100-\left(42+2\right)=56$

In the first draw, need to select the first tile of consonant from $100$ tiles. So, the probability of event $A$ is calculated as:

  $P\left(A\right)=\frac{56}{100}$

In the next draw, need to select the second tile of vowels from $99$ tiles. So, the probability of event $B$ is calculated as:

  $P\left(B\right)=\frac{42}{99}$

Now, the probability of the both events is calculated as:

  $\begin{array}{l}P\left(A\cap B\right)=P\left(A\right)\times P\left(B\right)\\ P\left(A\cap B\right)=\frac{56}{100}\times \frac{42}{99}\\ P\left(A\cap B\right)=0.2375\end{array}$