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Question

A coin is tossed n times. The probability of getting head atleast once is greater than 0.8, then the least value of n is


A

2

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B

3

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C

5

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D

4

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Solution

The correct option is B

3


An explanation for the correct option:

Step 1: Find the probability of getting head and getting tail.

We have been given that, a coin is tossed n times.

We need to find the value of n when the probability of getting head at least once is greater than 0.8

The probability of getting head is,p=12

The probability of getting tail is,q=12

Step 2: Find the probability of getting no head after n tosses.

Let X be the number of heads getting in n tosses.

We have been given that, the probability of getting head at least once is greater than 0.8

P(X1)0.8

So, the probability of getting no head i.e., X=0 would be,
P(X1)0.81-P(X=0)0.8P(X=0)1-0.8P(X=0)0.2

Step 3: Find the value of P(X=0) using Binomial distribution formula.

P(X=0)=C0n×(p)0×(q)n-0P(X=0)=n!0!(n-0)!×1×(12)nP(X=0)=1×1×(12)nP(X=0)=(12)n

Step 4: Find the value of n

P(X=0)0.2(12)n0.2(12)n(15)2n5

Let n=2,2n=22=4 which is not greater than or equal to 5.

Let n=3,2n=23=8 which is greater than or equal to 5.

This means, the least possible value of n is 3

Therefore, option(B) is the correct answer.


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