Chapter 7.3, Problem 55HP

To determine

To Find:

The probability that Patricia will roll an odd number and draw a letter in her name.

Answer to Problem 55HP

G

Explanation of Solution

Given Information:

For a game, Patricia must roll a standard die and draw a card from a deck of 26 cards, each card having a letter of the alphabet on it.

Concept Used:

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

  $\begin{array}{l}P\left(A\cap B\right)=P(A)\cdot P(B)\\ where\\ P(A)=\text{Probability of event A}\\ \text{P(B) = Probability of event B}\end{array}$

Calculation:

  $\begin{array}{l}Let\\ A\text{ = event of getting an odd number on the die}\text{.}\\ \text{B = event of drawing a letter from the name 'Patricia'}\\ \text{Total numbers on a dice = {1,2,3,4,5,6}= 6}\\ Odd\text{ numbers on the dice = {1,3,5}=3}\\ \text{Then Probability of A = }\frac{N\text{umber of favourable outcomes}}{Total\text{ number of outcomes}}=\frac{3}{6}=\frac{1}{2}\\ N\text{umber of different letters in the name 'Patricia' = 6}\\ \text{Total number of letters = 26}\\ \text{Probability of B = }\frac{N\text{umber of favourable outcomes}}{Total\text{ number of outcomes}}=\frac{6}{26}\\ P(A)=\frac{1}{2}\\ P(B)=\frac{6}{26}\\ We\text{ need to find the probability that Patricia will roll an odd number and draw a }\\ \text{letter in her name}\text{.}\\ \text{It is the intersection of both the above events}\text{.}\\ \text{So, P(A}\cap \text{B)=P(A)}\cdot \text{P(B)=}\frac{1}{2}\cdot \frac{6}{26}=\frac{3}{26}\\ Therefore,\text{ the correct option is G}\text{.}\end{array}$