Question

A pair of dice is thrown 5 times. If the probability of getting a doublet twice is $P\left(A\right),$ then the value of $3888\times P\left(A\right)=$

• A. 625
• B. 225
• C. 25
• D. 55

Answer 1

The correct option is A 625

Let us look at the experiment mentioned in the question. We are throwing a pair of dice and we are repeating that 5 times. The event we are interested in is getting a doublet two times.
When we throw a pair of dice, what is the probability of getting a doublet? Any pair of the form $(x,x)$ is a doublet. There are 6 possible doublets and 36 possible outcomes when we throw a pair of dice. So the probability of getting a doublet would be $\frac{6}{36}=\frac{1}{6}$
We want to find the probability of getting doublet in 2 out of the 5 trials. This is same as finding probability of r successes in n trials, which would be equal to ${}^n{C}_r{p}^r{q}^{n-r}$, where $p$ is the probability of success and $q$ is the probability of failure. In our example, $p=\frac{1}{6}$ and $q=\frac{5}{6}$
So, the probability of 2 successes(two doublet) in 5 trials is given by ${}^5{C}_2{\left(\frac{1}{6}\right)}^2{\left(\frac{5}{6}\right)}^3$
$=\frac{625}{3888}$
$\Rightarrow 3888\times P\left(A\right)=625$