What Is the Probability That Three Men Will Take the Same Driving Test?

[Jason Stock]

Homework Statement

What is the probability the 3 men take the same test?
A driving exam has 5 different written driving tests to give to drivers. Two women and three men take the test. What is the probability of each event?

a) the 3 men take the same test

b) exactly 3 people take the same test

c) all 5 people take a different test

Homework Equations

none here

The Attempt at a Solution

for (a) first guy can take any test. The probability that the next man takes the same test is 1/5, and the probability that the third man takes the same test is 1/5 again? Atleast that's what I think. I am so confused and time is running out for me...

Homework Statement

 

[Dick]

That's a good start for the first one. So what is the probability the 3 men take the same test? Now what do you think about the other ones?

 

[Jason Stock]

b) Take the probability from a. and multiply it by

(5*4*3)/(3*2*1) = 10
P = 10/25 = 2/5

c) The first person can take any test. The probability that the second takes a different test is 4/5, the probability that the third takes a different test is 3/5, that the fourth takes a different test 2/5, and that the fifth takes still a different test is 1/5??

P = (4/5)*(3/5)*(2/5)*(1/5)

I really don't know if this is even right. i just don't feel clear on this all. Please help me out?

 

[Dick]

b) Take the probability from a. and multiply it by

(5*4*3)/(3*2*1) = 10
P = 10/25 = 2/5

c) The first person can take any test. The probability that the second takes a different test is 4/5, the probability that the third takes a different test is 3/5, that the fourth takes a different test 2/5, and that the fifth takes still a different test is 1/5??

P = (4/5)*(3/5)*(2/5)*(1/5)

I really don't know if this is even right. i just don't feel clear on this all. Please help me out?

You are doing better than you think. c) is right. b) is still a bit off. You didn't explain all of your reasoning in b), but you didn't make sure the other two people you've haven't selected don't take the same test as the three you did. The question says 'exactly three'.

 

[Jason Stock]

You are doing better than you think. c) is right. b) is still a bit off. You didn't explain all of your reasoning in b), but you didn't make sure the other two people you've haven't selected don't take the same test as the three you did. The question says 'exactly three'.

i've no idea what to do next or how to finish this off. sorry for being stupid...

 

[Dick]

i've no idea what to do next or how to finish this off. sorry for being stupid...

Stop saying you are stupid and start thinking. You picked all groups of three people and multiplied by the probability they all take the same test. What's the probability the other two people didn't take the same test? You have to multiply by that too.

 

[Jason Stock]

ok... so a. and c. are right, b I'm half right and just need to do the same thing?

 

[Dick]

ok... so a. and c. are right, b I'm half right and just need to do the same thing?

What's the probability that the two you didn't pick don't take the same test as the three you did. Multiply by that and I think you are right.