Question

What is the probability that there will be more than 1 and less than 4 odd numbers in 5 rolls of a dice?

Answer 1

Probability of odd number in a throw of dice = 1/2
Probability of not getting odd number in a throw of dice = 1/2
Now ,
By binomial distribution P = nCr*(p^r)*(q^(n-r))
where p = probability of success in one outcome
            q = probability of failure in one outcome
Probability of getting one odd number in 5 rolls = 5C1*[(1/2)^1]*[(1/2)^4]
P = 5*(1/2)*(1/16)
P =5/32

Answer 2

Number of odd numbers less than 4 and more than 1  = 2.3
thus either 2 odd numbers will be there or 3

thus probability when a dice is thrown 5 times =  3C2 * 3C3  /  5C2
                                                                          =  3 / 10
thus the probability is 3/10