Question

(1 point) 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 0.15.

Due to his various superstitions, he is 4-times more likely to use 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.

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(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?  

equation editor

(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?  

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(use four decimals)

Answer 1

ANSWER::

Given,

From the given information

P(A) = 4*P(B)

Let us consider,

P(A) + P(B) = 1

4*P(B) + P(B) = 1

5*P(B) = 1

P(B) = 1/5

P(B) = 0.2

P(A) = 1 - P(B)

= 1 - 0.2

P(A) = 0.8

So the probability that he will use his brand A hockey stick is 0.8

b)

To determine the probability that the stick he uses at the start of the game breaks

the probability that the stick he uses at the start of the game breaks = P(Brand A & breaks + B & breaks)

= 0.8*0.09 + 0.2*0.15

= 0.072+ 0.03

= 0.102

Hence the probability that the stick he uses at the start of the game breaks is 0.102

c)

To determine the probability that he started the game with Brand B

= P(Brand B & breaks) / P(Breaks)

= 0.2*0.15 / 0.102

= 0.03 / 0.102

= 0.2941

Hence the probability that he started the game with Brand B is 0.2941

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