The Northside Rifle Team has two markspersons, Ralph and Sally. Ralph hits a bul

Question

The Northside Rifle Team has two markspersons, Ralph and Sally. Ralph hits a bull’s eye 90% of the time, and Sally hits a bull’s eye 95% of the time.

What is the probability that either Ralph or Sally both will hit the bull’s eye if each takes one shot?

What is the probability that Ralph and Sally will both hit the bull’s eye?

Did you make any assumptions in answering the preceding questions? If you answered yes, do you think you were justified in making the assumptions?
Display calculations in an Excel Spreadsheet format.

Explanation / Answer

Let's define event,

A : Ralph hits a bull’s eye

B : Sally hits a bull’s eye .

P( A ) = 0.9 P( B ) = 0.95

a ) P(  Ralph or Sally both will hit the bull’s eye) = P( A or B)

P( A or B ) = P( A ) + P( B ) - P( A and B )

=P(A ) + P(B) - P( A ) P(B) { Since A and B are independent events then

P(A and B ) = P(A)P(B) }

= 0.9 + 0.95 - 0.9*0.95 = 0.995

P(  Ralph or Sally both will hit the bull’s eye) = 0.995

b) P(Ralph and Sally will both hit the bull’s eye) = P( A and B)

P( A and B ) = P( A ) P( B) { Since A and B are independent events }

= 0.9*0.95 = 0.855

P(Ralph and Sally will both hit the bull’s eye) = 0.855

c ) To find previous probabilities we need to make assumtion that two events are independent .

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