Question

y ou roll a die 11 times. Success is defined as rolling a 4.

a. How many identical trials do we have for this problem?

b. What is the probability of success on the first trial?

c. What is the probability of rolling 4 three times?

Answer 1

Here success is rolling a 4 . In a die probability of rolling a 4 is 1/6.

So probability of success is p= 1/6

a. Here we are rolling the die 11 Times.

So number of identical trials is 11 .

b. Here the rolling of die is independent of each trials .

In the 1st trial probability of rolling a 4 is 1/6 . So probability of success on 1st trial is 1/6 or 0.1667 .

c. Here number of trials n= 11

Probability of rolling a 4 = p = 1/6

Let , X = number of rolling 4 .

Then we can say X ~ binomial (n,p) distribution

And P[X=x] =

We want

P[ X = 3 ] =

= 0.177656

Probability of rolling 4 three times is 0.177656 .