Game show there are 10 contestants of which 6 are female.

[AllenHe]

Homework Statement

At the start of a gameshow there are 10 contestants of which 6 are female. In each round of
the game, one contestant is eliminated. All of the contestants have the same chance of
progressing to the next round each time.

Given that the first contestant to be eliminated is male, find the probability that the next
two contestants to be eliminated are both female.

Homework Equations

p(next to be female|male)=(next to be female n male)/(male)

The Attempt at a Solution

I did (4/10)*(6/9)*(5/8)
But when I checked the answer, it was (6/9)*(5/8).
Why?

 

[Dick]

This is probably just a language issue. The problem says "Given that the first contestant to be eliminated is male". "Given" means that you assume the male is eliminated before you start calculating probabilities. It's called a conditional probability.

 

[AllenHe]

Ya, that's what I did. But how come I didn't get the same answer?

 

[AllenHe]

Or is there something wrong with my equation?

 

[Dick]

Or is there something wrong with my equation?

"Given" means something has already taken place and you don't factor in that probability. There's nothing wrong with the equation, but "given" means skip the 4/10 factor.

 

[HallsofIvy]

Originally, there were 10 contestants and 6 were female. Given that the first to be eliminated was male, there are now 9 contestants and 6 are female. What is the probability that the one eliminated now will be female? If that happens then there will be 8 contestants, 5 of them female. What is the probability that the one eliminated now will be female?

 

[AllenHe]

But how can I use the equation :

P(A|B)=P(AnB)/P(B)

to get the answer?Or is it not possible, because the total number of people decreases?

 

[Ray Vickson]

But how can I use the equation :

P(A|B)=P(AnB)/P(B)

to get the answer?Or is it not possible, because the total number of people decreases?

Sometimes we use that equation in reverse. When we know P(B) and P(A|B) we can use the equation to get P(AnB). That is what is happening in this problem.

RGV

 

[AllenHe]

so what's the value of P(AnB)?

 

[Ray Vickson]

so what's the value of P(AnB)?

Tell me what are A and B. You brought up the AnB, and I just responded to your question.

RGV

 

[AllenHe]

(4/10)*(6/9)*(5/8)
But it's not correct.

 

[Ray Vickson]

(4/10)*(6/9)*(5/8)
But it's not correct.

Of course not. As has already been explained clearly to you, there should be no 4/10 factor.

RGV

 

[ArcanaNoir]

so what's the value of P(AnB)?

the probability of two independent events A and B: P(AnB) is the probability of A times the probability of B. Thats two things, not three things. So, not (4/10)*(6/9)*(5/8). Just (6/9)*(5/8)