Mb12345678
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Hi, I really need help on this question - i have no clue where to start. It’s an AS statistics question.

In a game, a player can score 0, 1, 2, 3 or 4 points each time the game is played.
The random variable S, representing the player's score, has the following probability distribution where a, b and c are constants.

S 0 1 2 3 4
P(S=s) a b с 0.1 0.15
(This is a probability table)

The probability of scoring less than 2 points is twice the probability of scoring at least 2 points.
Each game played is independent of previous games played.
John plays the game twice and adds the two scores together to get a total.
Calculate the probability that the total is 6 points.
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ghostwalker
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(Original post by Mb12345678)
Hi, I really need help on this question - i have no clue where to start. It’s an AS statistics question.

In a game, a player can score 0, 1, 2, 3 or 4 points each time the game is played.
The random variable S, representing the player's score, has the following probability distribution where a, b and c are constants.

S 0 1 2 3 4
P(S=s) a b с 0.1 0.15
(This is a probability table)

The probability of scoring less than 2 points is twice the probability of scoring at least 2 points.
Each game played is independent of previous games played.
John plays the game twice and adds the two scores together to get a total.
Calculate the probability that the total is 6 points.
Use the given information to form a couple of simultaneous equations.

Can you do that to start?
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Mb12345678
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(Original post by ghostwalker)
Use the given information to form a couple of simultaneous equations.

Can you do that to start?
Ok thank you,

Could you do a+b+c+0.1+0.15=1 and 2(a+b)=c+0.25
And then work it out?
Last edited by Mb12345678; 2 months ago
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ghostwalker
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(Original post by Mb12345678)
Ok thank you,

Could you do a+b+c+0.1+0.15=1 and 2(a+b)=c+0.25
And then work it out?
Close.

Your first equation is correct.

For the second, P(S<2) = 2 P(S>=2), so your 2 mutlplier is on the wrong side of the equation.

Note that there is insufficient information to work out a and b, but that doesn't matter. You can work out c, and that's all you need for the remainder of the question.

Edit: Misspelt "insufficient"
Last edited by ghostwalker; 2 months ago
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Mb12345678
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(Original post by ghostwalker)
Close.

Your first equation is correct.

For the second, P(S<2) = 2 P(S>=2), so your 2 mutlplier is on the wrong side of the equation.

Note that there is sufficient information to work out a and b, but that doesn't matter. You can work out c, and that's all you need for the remainder of the question.
Oh right ok, i just thought that the P(S<2) is double that of P(S>=2)?

Anyway, thank you very much for the help
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Mb12345678
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(Original post by ghostwalker)
P(S<2) is double that of P(S>=2)

Yes, it is.

If y is double x, then y=2x.
Ohhhh that makes so much sense - i just thought of it the wrong way haha
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