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May 24th, 2018, 12:37 PM   #1
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Unhappy Calling all Stats wizards

Please oh great statistics wizards, help me not fail this assignment

A Statistics professor takes two hockey sticks - Brand A and Brand B - to each game he plays. Since Brand A is a newer stick than Brand B, so he believes the chance he will break his Brand A stick in a game is 9%; he also believes the probability he will break Brand B in a game is 0.13.

Due to his various superstitions, he is 2-times more likely to his Brand A hockey stick to start a game than the Brand B stick.

Part (a) Find the probability that he will use his Brand A hockey stick at the start of a hockey game. (use four decimals in your answer)

Part (b) Keeping in mind that he could use either Brand A or Brand B to start the game, what is the probability that the stick he uses at the start of the game breaks? (use four decimals)

Part (c) If he breaks the stick he started the game with, what is the probability that he started the game with Brand B? (use four decimals)
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May 28th, 2018, 01:42 AM   #2
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Imagine 3000 hockey games.

"He is 2-times more likely to use his Brand A hockey stick to start a game than the Brand B stick." So he uses A 2000 times and B 1000 times.

"He believes the chance he will break his Brand A stick in a game is 9%."
So he would break A .09(2000)= 180 times.

"He also believes the probability he will break Brand B in a game is 0.13."
So he would break B 0.13(1000)= 130 times.

"Part (a) Find the probability that he will use his Brand A hockey stick at the start of a hockey game. (use four decimals in your answer)"
That is 2000/3000= 0.6666

"Part (b) Keeping in mind that he could use either Brand A or Brand B to start the game, what is the probability that the stick he uses at the start of the game breaks? (use four decimals)"
Of the 2000 times he uses A it breaks 180 times and of the 1000 times he uses B it breaks 130 times. In all 3000 times, the hockey stick breaks 180+ 130= 310 times. The probability the hockey stick breaks is 310/3000= 0.1033.

"Part (c) If he breaks the stick he started the game with, what is the probability that he started the game with Brand B? (use four decimals)"
Of the 310 times the hockey stick broke, he was using B 130 times. Given that the hockey stick breaks, the probability he was using B is 130/310= 0.4193.
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