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Question

A coin is tossed 3 times.

The probability of obtaining at least two heads is


A

18

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B

38

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C

12

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D

23

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Solution

The correct option is C

12


An explanation for the correct option:

Step1. Use binomial distribution:

The binomial distribution is the discrete probability distribution that gives only two possible results in an experiment, either Success or Failure.

The formula for binomial distribution is:

P(x:n,p)=Cxnpx(q)1-x

Where,

n = the number of experiments

x=0,1,2,...

p = Probability of Success in a single experiment

q = Probability of Failure in a single experiment q=1-p

Step2. Find the required probability:

We have been given that a coin is tossed three times.

We need to find the probability of obtaining at least two heads.

Here, p=12,q=12,n=3

Since the coin is tossed three times and we need a sample space where at least two heads can be obtained.

So, X can takes values 2,3.

By using the binomial distribution, the probability of obtaining at least two heads is

P(X=2)+P(X=3)

=C23122123-2+C33123123-3=3!2!(3-2)!1412+3!3!(3-3)!18120=38+18=48=12

Hence, the correct option is (C).


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