A Statistics professor takes two hockey sticks - Brand A and Brand B - to each g

Question

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 10%; he also believes the probability he will break Brand B in a game is 0.12.

Due to his various superstitions, he is 3-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)

Explanation / Answer

let probability of using brand A or brand B Hockey are P(A) and P(B) respectively.

hence P(A)=3*P(B)

also

P(A)+P(B)=1

hence 3P(B)+P(B)=1

P(B)=0.25

and P(A)=0.75

hence probability that he will use his Brand A hockey stick =0.75

b)probability that the stick he uses at the start of the game breaks =P( brand A and breaks+brand B and breaks)

=0.75*0.1+0.25*0.12=0.105

c)probability that he started the game with Brand B given he breaks the stick =P(brand B and breaks)/P(breaks)

=0.25*0.12/0.105=0.2857

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