5 women are in a race. What is the probability that

I'll try to explain

all cases: 5! - total number of all combinations.

1. x ? ? ? ? (x is one of 3)


1st,2nd,3th,4th,5th
x - is not Sally and Jenny. 5-2=3 - another women
? - any woman beside x.
? ? ? ? - n=4! combinations.
therefore,


P=n/N= 4!*3/5!=3/5

2. 1 ? ? ? ?

1 - is Sally.
? - any woman beside 1.
? ? ? ? - n=4! combinations.
therefore,


p=m/N=4!/5!=1/5
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looks better

1.

Prob that Sally will not win = 4/5
Prob that Jeny will not win = 4/5

Hence 4/5 * 4/5 = 16/25

correct?

Here is my explanation:

1. for the first one its simple..what is the probability of both of them winning is 2/5

So the probability of them not winning is 1 - 2/5 = 3/5

2. for the second one...read the question in another way what is the probability of Sally winning

its 1/5 - I dont see why do you have to consider part of Jenny not winning.

I think this is the short cut way

Prob that Sally will not win = 4/5
Prob that Jeny will not win = 3/4(As Sally is already out of equation)

Hence 4/5 * 3/4 = 3/5

1)
p for Sally win the race = 1/5
p for Jenny win the race =1/5

p for all others win the race = 1-(1/5+1/5) =3/5

2) Sally win the race =1/5

What is OA?

Can someone explain the flaw here?

5 women are in a race.
What is the probability that Sally and Jenny both will not win the race?

Say S,J, X1,X2,X5 are in the race.. [ assuming the only one person will win the race out of 5 with equal probablity]
All these events[Winning S, Winning J, Winning X1.] are "mutually exclusive" --> Out comes are not common.
P(S) = 1/5
P(J) =1/5
P(X1)=1/5
P(X2)=1/5
P(X3)=1/5

probability of either one of them winning hte race
= P(S or J or X1 or X2 or X3) =P(S) +P(J)+P(X1)+P(X2)+P(X3) =1
probability that Sally and Jenny both will not win the race = probability that either one of X1 or X2 or X2 them win the race = P(X1)+P(X2)+P(X3) =1/5+1/5+1/5=3/5

check the below link, it may be useful for you.
https://www.regentsprep.org/regents/math/mutual/Lmutual.htm

Guess the question wording is not correct logically...

2 people can not win a race together... hence instead of saying..."probability that Sally and Jenny both will not win the race".. it should be "probability that Sally or Jenny both will not win the race"

Even with the second question - it should be - "What is the probability that Sally, will win the race?"... we don't need to specify not Jenny.. as Sally and Jenny cannot win the race at the same time