Question

1. raffle alfonso and cordell each bought one raffle ticket at the state fair. if 50 tickets were randomly sold, what is the probability that alfonso got ticket 14 and cordell got ticket 23?

Explanation:

Step1: Determine total possible outcomes

The total number of ways to assign 2 tickets to Alfonso and Cordell out of 50 is the number of permutations of 50 tickets taken 2 at a time, which is given by \( P(50, 2)=\frac{50!}{(50 - 2)!}=50\times49\)

Step2: Determine favorable outcomes

There is only 1 favorable outcome where Alfonso gets ticket 14 and Cordell gets ticket 23.

Step3: Calculate the probability

Probability \( P=\frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}=\frac{1}{50\times49}\)
Calculate \( 50\times49 = 2450\), so \( P=\frac{1}{2450}\approx0.000408\)

Answer:

The probability that Alfonso got ticket 14 and Cordell got ticket 23 is \(\frac{1}{2450}\) (or approximately \(0.000408\)).