Question

When a die is rolled k times, the expected frequency of getting a factor of 6 is 240. Then k=? Choose the answer following

A. 360 B.420 B.420 C.480 D.600 E. 720​

Answer 1

A. 360

Explanation:

The factors of 6 on a fair six-sided die are 1, 2, 3, and 6.

Therefore, the probability of getting a factor of 6 on a single roll of a fair six-sided die is:

`\begin{aligned}\sf Probability\:of\:an\:event\:occurring &= \sf (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)\\\\\sf \implies P(Factor\;of\;6)&=(4)/(6)\\\\&=(2)/(3)\end{aligned}`

Since each roll is independent, the probability of getting a factor of 6 on each roll is always 2/3.

The expected frequency is calculated by multiplying the probability of an event by the number of trials.

We are told that when a die is rolled k times, the expected frequency of getting a factor of 6 is 240. Therefore:

`\begin{aligned} \sf Expected\;frequency&=\sf Probability\;of\;event * Number\;of\;trials\\\\\implies 240&=(2)/(3)k\\\\240 \cdot (3)/(2)&=(2)/(3)k\cdot (3)/(2)\\\\360&=k\\\\k&=360 \end{aligned}`

Therefore, the value of k is 360.