Question

A 10-sided fair die with face numbers 0 through 9 is given.

What is the chance of getting at least 77 prime numbers (which are 2,3,5 and 7 on the die) when the die is rolled 150 times.

Answer 1

The prime numbers on a 10 sided die with numbers 0 through 9 are 2,3,5,7.

So, probability of getting a prime= 4/10= 0.4

Now our problem is clearly an application for BINOMIAL EXPERIMENT because

of the following reasons.

1)Number of rolls of die i.e number of trials = 150 is fixed.

2) all the rolls of die are independent and identical in the aspects of showing a prime number

3) considering a roll it results in either showing a prime (success) or not (failure).

4)probability of getting a prime i.e probability of success = 0.4 is same for every roll of die.

let X be the number of times that prime number  will be shown out of 150 rolls.

now we need to find P (X>=77).

Formula: P (X=x)= ncx.p^x . q^n-x .

Here n= 150, x = 77,78,79,.......150.

p=0.4,  q= 1-p = 0.6

P (X>=77) = 150cx . (0.4)^x . (0.6)^150-x .

= 0.0032 answer.