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edexcel S1 probablilty question

I'm having trouble with parts c) and d) of the following question!

Paul and Gill decide to play a board game. The probability that Paul wins the game is 0.25 and the probability that Gill wins is 0.3. They play 3 games. Results of successive games are independent. Find the probability that:

a)Paul wins all three games.
0.25 x 0.25 x 0.25 = 0.00156 (correct answer)
b)All games are drawn.
0.45 x 0.45 x 0.45 = 0.0911 (correct answer)
c)Gill wins two and paul wins one.
0.3 x 0.3 x 0.25 = 0.0225 (the answer is three times this - 0.0675, why do you multiply by three?
d)Each player wins one and the other game is drawn
0.25 x 0.3 x 0.45 = 0.03375 (the answer is six times this - 0.2025, why do you multiply by six?

The answers probably obvious and am probably gonna kick myself but any help will be appreciated :smile: cheers!
Original post by tdx
I'm having trouble with parts c) and d) of the following question!

Paul and Gill decide to play a board game. The probability that Paul wins the game is 0.25 and the probability that Gill wins is 0.3. They play 3 games. Results of successive games are independent. Find the probability that:

a)Paul wins all three games.
0.25 x 0.25 x 0.25 = 0.00156 (correct answer)
b)All games are drawn.
0.45 x 0.45 x 0.45 = 0.0911 (correct answer)
c)Gill wins two and paul wins one.
0.3 x 0.3 x 0.25 = 0.0225 (the answer is three times this - 0.0675, why do you multiply by three?
d)Each player wins one and the other game is drawn
0.25 x 0.3 x 0.45 = 0.03375 (the answer is six times this - 0.2025, why do you multiply by six?

The answers probably obvious and am probably gonna kick myself but any help will be appreciated :smile: cheers!


Think of the number of ways in which these events can occur :smile:
(edited 11 years ago)
You haven't counted all the possible combinations.
(edited 11 years ago)
Reply 3
Original post by Indeterminate
Think of the number of ways in which these events can occur :smile:



Original post by SherlockHolmes
You haven't counted all the possible combinations.


ahhhhh thank you! .. as predicted seems obvious now haha

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