Share
Notifications

View all notifications
Advertisement

The Least Number of Times a Fair Coin Must Be Tossed So that the Probability of Getting at Least One Head is at Least 0.8, is (A) 7 (B) 6 (C) 5 (D) 3 - Mathematics

Login
Create free account


      Forgot password?

Question

The least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is

Options
  • 7

  • 6

  • 5

  • 3

     

Solution

3

Let X denote the number of coins. 
Then, X follows a binomial distribution with

\[p = \frac{1}{2} , q = \frac{1}{2}\]
\[\text{ It is given that } P(X \geq 1) \geq 0 . 8\]
\[ \Rightarrow 1 - P(X = 0) \geq 0 . 8\]
\[ \Rightarrow P(X = 0) \leq 1 - 0 . 8 \]
\[ \Rightarrow P(X = 0) = 0 . 2\]
\[ \Rightarrow \frac{1}{2^n} \leq 0 . 2 \]
\[ \Rightarrow 2^n \geq \frac{1}{0 . 2}\]
\[ \Rightarrow 2^n \geq 5\]
\[\text{ This is possible when n } \geq 3\]
\[\text{ So, the least value of n is }  3 .\]

  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: 11 | Page no. 28
Advertisement

Video TutorialsVIEW ALL [1]

The Least Number of Times a Fair Coin Must Be Tossed So that the Probability of Getting at Least One Head is at Least 0.8, is (A) 7 (B) 6 (C) 5 (D) 3 Concept: Bernoulli Trials and Binomial Distribution.
Advertisement
View in app×