Chapter 3.4, Problem 36HP

To determine

To calculate: The probability that Liz draws a letter in her name and roll an odd number.

  $\begin{array}{l}F\frac{2}{3}\\ G\frac{1}{13}\\ H\frac{1}{26}\\ J\frac{3}{52}\end{array}$

Answer to Problem 36HP

The probability is option J $\frac{3}{52}$.

Explanation of Solution

Given information:

There is a deck of 26 cards and on each card one English alphabet is written. And an unbiased dice is there.

Formula used:

Probability of two events A and B happening simultaneously is $P\left(A\text{ and }B\right)=P\left(A\right)P\left(B\right)$.

Probability of an event is $\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}$.

Calculation:

Consider the provided information that there is a deck of 26 cards and on each card one English alphabet is written. And an unbiased dice is there.

So, probability that drawn card has letter in her name,

Probability of an event is,

  $\begin{array}{c}P=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}\\ =\frac{3}{26}\end{array}$.

There are 6 numbers on dice and there are three odd numbers.

So, probability that an old number comes is,

  $\begin{array}{c}P=\frac{\text{Number of possible outcomes}}{\text{Total number of outcomes}}\\ =\frac{3}{6}\end{array}$

Probability of two events A and B happening simultaneously is $P\left(A\text{ and }B\right)=P\left(A\right)P\left(B\right)$.

The probability that Liz draws a letter in her name and roll an odd number.

  $\begin{array}{c}P=\frac{3}{26}\cdot \frac{3}{6}\\ =\frac{3}{52}\end{array}$

Thus, the probability is option J $\frac{3}{52}$.