Question

A fair die is rolled nine times. What is the probability that

Answer 1

Answer:

The answer is 46/512 = 0.08984375

Step-by-step explanation:

In this question, success means to get an odd number on rolling a die.

The probability of success p = 3/6 = 1/2

So                                             p = 1/2

Now lets find probability of failure q

q = 1 - p = 1 - 1/2 = 1/2

So                                             q = 1/2

Let X  = x denotes the number of success in  n  trials.

So X  is a Binomial Random Variable

Which has the following parameters:

                                                n  = 9

as the fair die is rolled nine times and

                                                p = 1/2

Now the Probability of  x  success out of  n  trials P( X = x) is:

P(X = x) = p(x) =  nCx pˣ , qⁿ⁻ˣ , x= 0,1,2,...,9

P(X = x) = p(x) = nCx (1/2)⁹ = ₉Cₓ (1/2)⁹ = ₉Cₓ /512

Since the required probability is P (X < 3) So

P(X < 3) = P(X = 0) + P( X = 1) + P(X = 2)

             = 1 / 512 {₉C₀ + ₉C₁ + ₉C₂}                             nCr = n! / r! * (n - r)!

           

             = 1 / 512{ (9! / 0! * (9 - 0)!) + (9! / 1! * (9 - 1)!) + (9! / 2! * (9 - 2)!) }

             = 1 / 512 { 1 + 9 + 36 }

             = 46 / 512 =  0.08984375

So the required probability is 46/512