Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • NCERT
  • An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be atleast 4 successes.

Q. 9: An experiment succeeds twice as often as it fails. Find the probability that in the next six trials, there will be at least 4 successes.

Answers (1)

best_answer

probability of success is twice the probability of failure.

Let probability of failure be X

then Probability of success = 2X

The sum of probabilities is 1.

        \therefore \, \, \, X+2X=1

        \Rightarrow \, \, \, 3X=1

         \Rightarrow \, \, \, X=\frac{1}{3}

Let          P=\frac{1}{3}          and      q=\frac{2}{3}

Let X be random variable that represent the number of success in six trials.

\therefore \, \, \, \, P(X=x)=^nC_x.q^{n-x}.p^x

       P(X\geq 4)=P(X=4)+P(X=5)+P(X=6)

                             =^6C_4 \left [ \frac{2}{3} \right ]^4\left [ \frac{1}{3} \right ]^2+^6C_5 \left [ \frac{2}{3} \right ]^5\left [ \frac{1}{3} \right ]^1+^6C_6 \left [ \frac{2}{3} \right ]^6\left [ \frac{1}{3} \right ]^0

                          =\frac{15\times 2^4}{3^6}+\frac{6\times 2^5}{3^6}+\frac{2^6}{3^6}

                            =\frac{ 2^6}{3^6}(15+12+4)

                          =\frac{ 2^6}{3^6}(31)

                      =\frac{31}{9}\left [ \frac{2}{3} \right ]^4

Posted by

seema garhwal

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question