Answer:
P(X=1)=0.7 P(X=2)=0.233 P(X=3)=0.058 P(X=6)=0
Step-by-step explanation:
P(X=1) means that a man achieved the highest score.
7 out of 10 possible combinations have a man with the highest score, so P(X=1)=0.7.
P(X=2)
In this case, we have a woman in the first place and a man in the second place.
We have 3 combinations for the first place and 7 for the second place, out of 10!/(10-2)! possible combinations for the first and second place.
We can calculate P(X=2) as
[tex]P(x=2)=\frac{3*7}{10!/8!}=21/(10*9)=21/90 = 0.233[/tex]
P(X=3)
In this case, we have two women in the first and second place, and a man in the 3rd place.
We have 3*2 combinations for the 1st and 2nd places and 7 combinations for the 3rd place, out of 10!(10-3)! possible combinations for the 1st,2nd and 3rd places.
We can calculate P(X=3) as
[tex]P(x=3)=\frac{3*2*7}{10!/7!}=42/(10*9*8)=42/ 720= 0.058[/tex]
P(X=6)
In this case, we can say P(X=6) because there is only 3 women in the sample, so X must be 4 or smaller (P(X>4)=0).
