Advertisement

A Coin is Tossed 10 Times. the Probability of Getting Exactly Six Heads is - Mathematics

Question

A coin is tossed 10 times. The probability of getting exactly six heads is

Options
  • \[\frac{512}{513}\]

     
  • \[\frac{105}{512}\]

     
  • \[\frac{100}{153}\]

     
  • \[^{10}{}{C}_6\]

     

Solution

\[\frac{105}{512}\]

\[\text{ Let X denote the number of heads obtained in 10 tosses of a coin }  . \]
\[\text{ Then, X follows a binomial distribution with n = 6 } , p = \frac{1}{2} = q\]
\[\text{ The distribution is given by } \]
\[P(X = r) = ^{10}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{10 - r} \]
\[ \therefore P(X = 6) = \frac{^{10}{}{C}_6}{2^{10}}\]
\[ = \frac{105}{2^9}\]
\[ = \frac{105}{512}\]

  Is there an error in this question or solution?
Advertisement

APPEARS IN

Advertisement

Video TutorialsVIEW ALL [1]

A Coin is Tossed 10 Times. the Probability of Getting Exactly Six Heads is Concept: Bernoulli Trials and Binomial Distribution.
Advertisement
Share
Notifications

View all notifications
Login
Create free account


      Forgot password?
View in app×