Hello I am new to wyzant. I heard that you guys help. Please let this be true. Please help me with my math homework soon please!

Question

Each of 5 boys randomly chooses a watch from 12 different styles. What is the probability that at least 2 boys choose the same type of watch?

 

A.) ≈ 0.5387

B.) ≈ 0.7387

C.) ≈ 0.3819

D.) ≈ 0.6181

help

Answer 1

Ok. So we have 12 different styles of watches to choose from, so that means that the total number of combinations of styles for 5 boys is 12*12*12*12*12, since each boy has his pick of 12 options.

The way to answer this question is by way of the complementary rule: We want the number of ways that the boys can all have different styles. So the first boy to pick has 12 options available to him, the second boy has 11 options available to him, the 3rd boy has 10 options available to him, so on and so forth.

So the probability that the boys all have different watches is (12*11*10*9*8)/12^5= .3819.

To find the probability that at least two boys have the same style would just be 1-.3819=.6181, which is D.

I hope this helped.