Three contestants aim at a target in a throwing competition. If the probability that the first contestant hits the target is 1/3 and the probability that the second hits the target is 1/6 and the probability that the third hits the target is 1/4 ..

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2021-05-09
HebaAallahFathy

Three contestants aim at a target in a throwing competition. If the probability that the first contestant hits the target is 1/3 and the probability that the second hits the target is 1/6 and the probability that the third hits the target is 1/4 .Find the probability that:
If the target is hits by only one contestant.

الأجوبة

Let A be the event that the first contestant hits the target and B be the second contestant hits the target and C be the contestant hits the target, then:
P(A)=1/3   →P(A^c )=2/3
P(B)=1/6   →P(B^c )=5/6
P(C)=1/4   →P(C^c )=3/4
   Only one contestant hits the target mean that
A∩B^c∩C^c    or A^c∩B∩C^c   or A^c∩B^c∩C
     Let D be the event that only one contestant the target, then:
       D=(A∩B^c∩C^c )∪(A^c∩B∩C^c )∪(A^c∩B^c∩C)
∴P(D)=P(A∩B^c∩C^c )+P(A^c∩B∩C^c )+P(A^c∩B^c∩C)
=P(A)P(B^c )P(C^c )+P(A^c )+P(B)+P(C^c )+P(A^c )P(B^c )P(C)
=(1/3)(5/6)(3/4)+(2/3)(1/6)(3/4)+(2/3)(5/6)(1/4)
=31/72

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أسئلة مشابهة

Three horses in a race. The probability that the first horse is twice as likely to win as the second horse and the second horse is 3 times as likely to win as the third horse. Find the probability that the first horse or the second horse win.

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