Question

You and your friend enter a drawing with 4 different prizes. The prizes are awarded randomly. A total of 13 people enter the drawing.

1. In how many ways can you win first prize and your friend win second prize?

2. What is the probability that you win first prize and your friend wins second prize?

Answer 1

Answer:

1) 110

2) 0.00641

Step-by-step explanation:

1) 1×1×11×10 = 110

2) total = 13P4 = 17160

110/17160 = 1/156 or 0.00641

Answer 2

a) the number of ways you can win the first prize and your friend win the second prize = 110

b) the probability that you win first prize and your friend wins second prize = $\frac{1}{156}$

What is probability?

"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."

Formula of the probability of an event A is:

P(A) = n(A)/n(S)

where,  n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.

What is formula of permutation?

$^nP_r=\frac{n!}{(n-r)!}$

For given question,

You and your friend enter a drawing with 4 different prizes. The prizes are awarded randomly. A total of 13 people enter the drawing.

Total possible outcomes,

n(S) = $^{13}P_4$

Using the formula of permutation,

$^{13}P_4\\\\=\frac{13!}{(13-4)!} \\\\=17160$

Hence, n(S) = 17160

Let event A: you can win the first prize and your friend win the second prize

So, the number of ways you can win the first prize and your friend win the second prize are,

n(A) =  1×1×11×10

n(A) = 110

And the probability that you win first prize and your friend wins second prize would be,

$P(A)=\frac{n(A)}{n(S)}\\\\ P(A)=\frac{110}{17160}\\\\ P(A)=\frac{1}{156}$

Therefore, a) the number of ways you can win the first prize and your friend win the second prize = 110

b) the probability that you win first prize and your friend wins second prize = $\frac{1}{156}$

Learn more about probability here:

brainly.com/question/11234923

#SPJ3