 ## Book: RD Sharma - Mathematics (Volume 2)

### Chapter: 33. Binomial Distribution

#### Subject: Maths - Class 12th

##### Q. No. 31 of Exercise 33.1

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31
##### An unbiased coin is tossed 8 times. Find, by using binomial distribution, the probability of getting at least 6 heads.

Let x be the number of heads in the tosses.

Let n be the total number of tosses.

Then, binomial distribution is given by

P (X = x) = nCxpxqn-x

Where x = 1, 2, 3, …, n

Here, p = probability of getting a head.

And q = probability of getting a tail. Then, We need to find the probability of getting at least 6 head.

Then, x = 6, 7, 8 [ there are 8 number of tosses]

First, putting n = 8 & x = 6. We get      …(i)

Now, putting n = 8 & x = 7. We get     …(ii)

Now, putting n = 8 & x = 8. We get     …(iii)

The probability of getting at least 6 heads is given by

Probability = P(6) + P(7) + P(8)

Substituting values in (i), (ii) & (iii) in above equation. We get    Thus, the probability of getting at least 6 heads is .

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