Probability 5 Question 6

6. If the probability of hitting a target by a shooter in any shot, is 13, then the minimum number of independent shots at the target required by him so that the probability of hitting the target at least once is greater than 56, is

(2019 Main, 10 Jan II)

(a) 6

(b) 3

(c) 5

(d) 4

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Answer:

Correct Answer: 6. (c)

Solution:

  1. The probability of hitting a target at least once =1( probability of not hitting the target in any trial) =1nC0p0qn

where n is the number of independent trials and p and q are the probability of success and failure respectively.

[by using binomial distribution]

Here, p=13 and q=1p=113=23

According to the question, 1nC013023n>56

23n<15623n<16

Clearly, minimum value of n is 5 .



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