rauls favorite restaurant is running a prize game. five of each of the winning tickets shown are available…

rauls favorite restaurant is running a prize game. five of each of the winning tickets shown are available, and a customer must collect three winning tickets to receive the prize. what is the probability raul will receive the prize for the baseball cap with his first 3 tickets?\nthe probability raul will receive the baseball cap prize is \n(type an integer or a simplified fraction.)

rauls favorite restaurant is running a prize game. five of each of the winning tickets shown are available, and a customer must collect three winning tickets to receive the prize. what is the probability raul will receive the prize for the baseball cap with his first 3 tickets?\nthe probability raul will receive the baseball cap prize is \n(type an integer or a simplified fraction.)

Answer

Explanation:

Step1: Calculate total number of tickets

There are 4 types of prizes and 5 tickets of each type, so the total number of tickets is $4\times5 = 20$ tickets.

Step2: Calculate number of favorable outcomes

There are 5 tickets for the baseball - cap prize. The number of ways to choose 3 tickets out of the 5 baseball - cap prize tickets is given by the combination formula $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 5$ and $r=3$. $C(5,3)=\frac{5!}{3!(5 - 3)!}=\frac{5!}{3!2!}=\frac{5\times4}{2\times1}=10$.

Step3: Calculate number of total outcomes

The number of ways to choose 3 tickets out of 20 tickets is $C(20,3)=\frac{20!}{3!(20 - 3)!}=\frac{20\times19\times18}{3\times2\times1}=1140$.

Step4: Calculate probability

The probability $P$ is the number of favorable outcomes divided by the number of total outcomes. So $P=\frac{C(5,3)}{C(20,3)}=\frac{10}{1140}=\frac{1}{114}$.

Answer:

$\frac{1}{114}$