Bays Theorem

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A basketball coach of the local University team is doing some research on the teams historical record for the past few years. During that time, the team has had a star player, Mike Jones (otherwise known as 'MJ'). Not only is MJ a great player but he also gives the team a morale boost when he plays. In fact, looking at the team's records, the coach notes that:

Of all the wins the team has had, 75% of the time MJ was playing in the game, while 25% of the time he wasn't.
Of all the losses the team has had, only 35% of the time was MJ playing in the game, while the other 65% of losses he wasn't.
Also, the coach works out that during the time MJ has been with the team, the team has had a win rate of 60%.

Today the team play a game and MJ has shown up to play. Assuming all other things being equal, and based on the above information, find the probability that the team wins today's game. Give your answer as a decimal to 2 decimal places.

Probability that the team wins =

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View best answer, chosen by klazman

@klazman,

I don't like to do homework unless I am the one getting the grade. But, I don't mind helping you if you want to take a stab at it.

Why don't you start by writing Bayes Theorem... and see if you can write down the relevant variables. Then I can tell you if you are on the right track.

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@klazman,

From Bayes Theorem, P(A|B) = P(B|A)*P(A)/P(B)

If A is team winning and B is MJ playing, then
P(B|A) is the probability of winning when MJ is playing = 75%
P(A) is the probability of winning in general = 60%
P(B) is the probability of MJ playing in the game which is not given.

We need to find P(B). MJ plays in 75% of the wins (60%) and 35% of the losses (40%). 75% x 60% + 35% x 40% = 59%

Back to the formula, Probability of winning given MJ is playing is 75% x 60% / 59% = 0.76

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@engineer,

Good, at least one of us likes doing other people's homework for them.

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@engineer,

Thank you engineer. You will never know the impact of what you just did for me.

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@engineer,

While this was a good calculation, you made it a little confusing when saying "the game" rather than "any given game". There's a serious difference there and linguistic accuracy regarding the events queried helps minimize confusion, but of course, no disrespect intended.

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Bays Theorem

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