Answer to Question #165030 in Statistics and Probability for Bradley Smothermon

Question

A jar contains 8 pennies, 4 nickels and 4 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins. Find the probability X=10

Answer 1

Given coins are , 8 pennies, 4 nickels, 4 dimes

As X denote the amount of cents in selected coins

$10 \text{ cents}=2 \text{ nickels}$

So probability of (X=10), contains withdrwal of 2 nickels without replacement

Probability of drawing first nickel =$\dfrac{4}{16}$

Probability of drawing second nickel =$\dfrac{3}{15}$

$\implies P(X=10)=(\dfrac{4}{16})(\dfrac{3}{15})=\dfrac{1}{20}$

Hence, Probability $(X=10)$ is $\dfrac{1}{20}.$