Question

Mark the correct alternative in each of the following:

An unbiased dice was rolled 800 times simultaneously. The frequencies of the various outcomes are given in the table below :

Outcome : 1 2 3 4 5 6

Frequency : 150 200 100 75 125 150
When the dice is rolled, the probability of getting a number which is a perfect square is

$$\begin{gathered} \left(\mathrm{a}\right)\frac{9}{32} \\ \left(\mathrm{b}\right)\frac{11}{32} \\ \left(\mathrm{c}\right)\frac{13}{32} \\ \left(\mathrm{d}\right)\frac{15}{32} \end{gathered}$$

Answer 1

It is given that an unbiased dice was rolled 800 times.

∴ Total number of trials = 800

Let E be the event of getting a number on the dice which is a perfect square.

Now, 1 and 4 are perfect squares among the outcomes 1, 2, 3, 4, 5 and 6.

∴ Number of trials of getting a number which is perfect square on the dice

= Frequency of getting 1 or 4 on the dice

= 150 + 75

= 225

So, P(Getting a number which is perfect square) = P(E) = $\frac{\mathrm{Number}\mathrm{of}\mathrm{trials}\mathrm{of}\mathrm{getting}\mathrm{a}\mathrm{number}\mathrm{which}\mathrm{is}\mathrm{perfect}\mathrm{square}}{\mathrm{Total}\mathrm{number}\mathrm{of}\mathrm{trials}}=\frac{225}{800}=\frac{9}{32}$

Thus, the probability of getting a number which is a perfect square is $\frac{9}{32}$.

Hence, the correct answer is option (a).