HSC Arts 12th Board ExamMaharashtra State Board
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# The Probability that a Bomb Will Hit a Target is 0.8. Find the Probability that Out of 10 Bombs Dropped, Exactly 4 Will Hit the Target. - HSC Arts 12th Board Exam - Mathematics and Statistics

ConceptBernoulli Trials and Binomial Distribution

#### Question

The probability that a bomb will hit a target is 0.8. Find the probability that out of 10 bombs dropped, exactly 4 will hit the target.

#### Solution

Let r = no of bombs hit the target

p=0.8

q=0.2            (1-p=q)

n=10            r=4

p(r=4)=""^nC_rp^rq^(n-r)      r=0,1,2...........,n

=""^10C_4(0.8)^4(0.2)^6

=""^10C_4(8/10)^4(2/10)^6

=(10!)/(4!6!) xx(2)^18(1/10)^10

=(10xx9xx8xx7)/(4xx3xx2)xx(2)^18xx(1/10)^10

=210xx(2)^18xx(1/10)^10

=(262144xx210)/(10)^10=55050240/(10)^10

=Anti[log210+18log2-10]

=Anti[2.3222+18log(0.3010)-10]

=Anti(3.7402)

=0.0055

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#### APPEARS IN

2016-2017 (March) (with solutions)
Question 4.2.5 | 2.00 marks

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Solution The Probability that a Bomb Will Hit a Target is 0.8. Find the Probability that Out of 10 Bombs Dropped, Exactly 4 Will Hit the Target. Concept: Bernoulli Trials and Binomial Distribution.
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