The Northside Rifle team has two market The Northside Rifle team has two markspe

Question

The Northside Rifle team has two market The Northside Rifle team has two markspersons, Dick and Sally. Dick hits a bull's-eye 90% of the time, and Sally hits a bull's-eye 95% of the time. (a) What is the probability that either Dick or Sally or both will hit the bull's-eye if each takes one shot? (b) What is the probability that Dick and Sally will both hit the bull's-eye? (c) Did you make any assumptions in answering the preceding questions? If you answered yes, do you think that you are justified in making the assumption(s)?

Explanation / Answer

SOLUTION:
(a)The probability that either Dick or Sally or both will hit the bull’s eye if each takes one
=>let, Dick=Event A
Sally=Event B
So,
P (A)+P (B) – P (A and B) = 0.9 + 0.95 - 0.855 = 0.995 OR 99.5% of time either dick or sally or both will hit the bull's -eye
we can say this in other way also like in term of misses:
1-{P(NA)*P(NB)}=1-(0.1*0.05)=1-0.005=0.995 OR 99.5% chance of not missing

(b)The probability that dick and sally will both hit the bull’s eye:

=> P (A) * P(B) = 0.9 x 0.95 = 0.855 OR 85.5% of the time dick and sally will both hit the bull's-eye
here joint probability of mulitple ,independent events occurring at the same time

=> (c) Yes the assumption that the events are independet because Dick's marksmanship would not affect Sally's and same as sally's marksmanship not affect Dick's as they each had a record of performance.

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