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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

\[= P\left( X \leq 6 \right)\]

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

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

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

\[ = 1 - \frac{9}{256}\]

\[ = \frac{247}{256}\]

  Is there an error in this question or solution?
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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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Solution A Fair Coin is Tossed 8 Times, Find the Probability Of At Most Six Heads. Concept: Introduction of Probability.
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