Please can you help me with my maths question and please can you tell me how you worked it out?

Question

When jaqui and wendy play tennis the probability of jaqui winning is 3/4 and the probability of Wendy winning is 1/4.
When jaqui and wendy play a game of chess the probability of Jaqui winning is 1/5 therefore making Wendy's chance of winning 4/5 and like tennis one of the two girls MUST win assume there is no chance of a draw in a game of chess

work out the probability of

i)Jaqui winning both games
ii)Wendy winning at least one of the games
iii)the girls winning 1 game each

Answer 1

1. The probability of J winning both games is P(J,tennis)*P(J,chess) = 3/4 * 1/5 = 3/20

2. The probability of Wendy winning at least one game is
1 - (Probability of J winning both games )
= 1 - 3/20
= 17/20.

3. The girls winning one game each
= 1 - probability of J winning both - Probability of W winning both
= 1 - 3/20 - 1/5
= 17/20 -4/20
= 13/20

Answer 2

You can make a "probability tree" to solve this.
You can start with the tennis; you have 2 branches, the prob that Jaqui wins and the prob that Wendy wins. Each branch then has two branches, for example, the branch that Jaqui wins tennis has the branches that she wins chess and
she loses chess. The prob of a tennis win is 3/4 and of a chess win is 1/5th. The probability of BOTH is 3/20. By doing the same with the other branches, you can figure out the probabilities.

Answer 3

First, remember this:

And = multiplication
Or = addition

I) .15

Jaqui must win both tennis AND chess.

3/4 * 1/5 = .15

II) .85

When solving for At Least problems, always do 1- the probability that is NOT possible.

For example, for Wendy to win at least 1 game, there is a chance that she wins only tennis, a chance that she wins only chess, and a chance that she wins both.

It is NOT possible for her to lose both.

1-(probability of jaqui losing tennis AND probability of jaqui losing chess)

1-(3/4*1/5)

III) .8

Again, use the And & Or.

For this to be true,

Jaqui must win tennis (3/4) AND Wendy must win chess (4/5)

OR

Wendy must win tennis (1/4) AND Jaqui must win chess (3/4)


(3/4) * (4/5) + (1/4) * (3/4)



When solving probability problems, try and word it out in English, and replace the terms with operators, it truly helps.

Hope this helped, if I'm wrong, I apologize, although I'm pretty sure that this is correct.