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# GCSE - Probability watch

1. Mr Lucky plays two games.
The two games are Game A and Game B.
Playing Game A and Game B are independent events.
The probability that Mr Lucky wins both games is 9/25.
The probability that Mr Lucky wins Game B is four times greater than the probability of him losing Game A.
Find the probability that Mr Lucky wins only one of the two games he plays.

So I know that P(winA)×P(winB) = 9/25, and that P(winB)=4P(loseA), but I'm not exactly sure how to progress? Any help is appreciated.
2. Make 2 tree diagrams, one Game A and one Game B,
remembering that they are independent events.
Call P(Win A) ‘x’ and the P(Lose A) ‘1-x’.

From here you know that the probability of him winning game B is 4 times the probability of him losing game A. From this you can write down the probability of him losing game B.

Form a quadratic that is equal to 9/25 and solve for ‘x’.

Can you take it from here?
3. (Original post by Y11_Maths)
Make 2 tree diagrams, one Game A and one Game B,
remembering that they are independent events.
Call P(Win A) ‘x’ and the P(Lose A) ‘1-x’.

From here you know that the probability of him winning game B is 4 times the probability of him losing game A. From this you can write down the probability of him losing game B.

Form a quadratic that is equal to 9/25 and solve for ‘x’.

Can you take it from here?
Got it - thank you
4. (Original post by irrelevant kid)
Got it - thank you
5. (Original post by Y11_Maths)
P(lose A) = x
P(win A) = 1-x
P(win B) = 4x

4x × 1-x = 4x-4x^2
4x-4x^2 = 9/25
Multiply and rearrange:
100x^2-100x+9=0
(10x-1)(10x-9)=0
x=1/10 or x=1/9
Used 1/10 as worked.

Win A, lose B = 54/100
Lose A, win B = 4/100
P(win only one) = 58/100 = 29/50

Going to bed now, so if I've done anything wrong just reply and I'll correct tomorrow.
Thanks for helping by the way, I appreciate it.
6. (Original post by irrelevant kid)
P(lose A) = x
P(win A) = 1-x
P(win B) = 4x

4x × 1-x = 4x-4x^2
4x-4x^2 = 9/25
Multiply and rearrange:
100x^2-100x+9=0
(10x-1)(10x-9)=0
x=1/10 or x=1/9
Used 1/10 as worked.

Win A, lose B = 54/100
Lose A, win B = 4/100
P(win only one) = 58/100 = 29/50

Going to bed now, so if I've done anything wrong just reply and I'll correct tomorrow.
Thanks for helping by the way, I appreciate it.
This is correct well done. And I am happy to help anytime

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