Question:

A pair of dice is thrown 3 times. If getting a doublet is considered a success, then the probability of two successes is :

Updated On: May 13, 2025
  • \(\frac{1}{72}\)
  • \(\frac{7}{72}\)
  • \(\frac{5}{72}\)
  • \(\frac{11}{72}\)
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is C

Solution and Explanation

Let's calculate the probability of getting a doublet when a pair of dice is thrown. A doublet occurs when both dice have the same number. The possible doublets are: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). Thus, there are 6 favorable outcomes for doublets out of 36 total outcomes when two dice are thrown. The probability \(P\) of getting a doublet in a single throw is:
\(P(\text{doublet})=\frac{6}{36}=\frac{1}{6}\)
We need to find the probability of getting exactly two successes (doublets) in 3 throws. This is a binomial distribution problem where the number of trials \(n=3\), the number of successes \(k=2\), and the probability of success \(p=\frac{1}{6}\).
The probability \(P(X=k)\) of getting exactly \(k\) successes in \(n\) trials is given by the binomial probability formula:
\(P(X=k)=\binom{n}{k}p^k(1-p)^{n-k}\)
Substituting \(n=3\), \(k=2\), and \(p=\frac{1}{6}\):
\(P(X=2)=\binom{3}{2}\left(\frac{1}{6}\right)^2\left(\frac{5}{6}\right)^{1}\)
\(\binom{3}{2}=3\), thus:
\(P(X=2)=3\times\left(\frac{1}{36}\right)\times\left(\frac{5}{6}\right)\)
\(P(X=2)=\frac{15}{216}=\frac{5}{72}\)
The correct answer is \(\frac{5}{72}\).
Was this answer helpful?
0
0

Top Questions on Probability

View More Questions