Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
Share
Notifications

View all notifications
Advertisement

A Coin is Tossed 4 Times. the Probability that at Least One Head Turns up is - Mathematics

Login
Create free account


      Forgot password?

Question

A coin is tossed 4 times. The probability that at least one head turns up is

Options
  • \[\frac{1}{16}\]

     
  • \[\frac{2}{16}\]

     
  • \[\frac{14}{16}\]

     
  • \[\frac{15}{16}\]

     

Solution

\[\frac{15}{16}\]

Let X denote the number of heads obtained in four tosses of a coin .
Then X follows a binomial distribution with

\[n = 4 \text{ and } p = q = \frac{1}{2}\]
\[\text{ Distribution is given by } \]
\[P(X = r) = ^{4}{}{C}_r \left( \frac{1}{2} \right)^r \left( \frac{1}{2} \right)^{4 - r} \]
\[ \therefore P(X = r) = ^{4}{}{C}_0 \left( \frac{1}{2} \right)^0 \left( \frac{1}{2} \right)^{4 - 0} \]
\[P(\text{ atleast one head turns up} )  = P(X \geq 1) \]
\[ = 1 - P(X = 0) \]
\[ = 1 - \frac{1}{2^4}\]
\[ = \frac{15}{16}\]

  Is there an error in this question or solution?
Advertisement

APPEARS IN

 RD Sharma Solution for Mathematics for Class 12 (Set of 2 Volume) (2018 (Latest))
Chapter 33: Binomial Distribution
MCQ | Q: 22 | Page no. 29
Advertisement

Video TutorialsVIEW ALL [1]

A Coin is Tossed 4 Times. the Probability that at Least One Head Turns up is Concept: Bernoulli Trials and Binomial Distribution.
Advertisement
View in app×