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# A Fair Coin is Tossed 8 Times, Find the Probability Of At Most Six Heads. - Mathematics

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#### Question

A fair coin is tossed 8 times, find the probability of at most six heads.

#### Solution

Let X denote the number of heads obtained when a fair is tossed 8 times.
Now, X is a binomial distribution with n = 8, $p = \frac{1}{2}$ and  $q = 1 - \frac{1}{2} = \frac{1}{2}$

$\therefore P\left( X = r \right) =^8 C_r \left( \frac{1}{2} \right)^{8 - r} \left( \frac{1}{2} \right)^r =^8 C_r \left( \frac{1}{2} \right)^8 , r = 0, 1, 2, . . . , 8$

Probability of getting at most 6 heads

$= P\left( X \leq 6 \right)$

$= 1 - \left[ P\left( X = 7 \right) + P\left( X = 8 \right) \right]$

$= 1 - \left[ {}^8 C_7 \left( \frac{1}{2} \right)^8 +^8 C_8 \left( \frac{1}{2} \right)^8 \right]$

$= 1 - \left( \frac{8}{256} + \frac{1}{256} \right)$

$= 1 - \frac{9}{256}$

$= \frac{247}{256}$

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#### APPEARS IN

RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 33: Binomial Distribution
Ex. 33.1 | Q: 5.3 | Page no. 13
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#### Video TutorialsVIEW ALL [1]

Solution A Fair Coin is Tossed 8 Times, Find the Probability Of At Most Six Heads. Concept: Introduction of Probability.
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