Question

Three six – faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is 

k (3 ≤ k ≤ 8) is

Solution

Correct option is

The total number of cases is 6 × 6 × 6 = 63 = 216. The number of favorable ways

                   = coefficient of xk in (x + x2 +…….+ x6)3

                   = coefficient of xk – 3 in (1 – x6)3 (1 – x) – 3

                   = coefficient of xk – 3 in (1 – x) – 3                 [∴ 0 ≤ k – 3 ≤ 5]

                   = coefficient of xk – 3 in 

                  

Thus, the probability of the required event is (k – 1) (k – 2)/432

SIMILAR QUESTIONS

Q1

The minimum number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8 is

Q2

For the three events AB and CP(exactly one of the events A or Boccurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs) = p and P (all the three events occur simultaneously) = p2, where 0 < p < 1/2. Then the probability of at least one of the three events AB and C occurring is

Q3

Nine identical balls are numbers 1, 2,…9. Are put in a bag. A draws a ball and gets the number a. the ball is put back the beg. Next B draws a ball gets the number b. The probability that a and b satisfies the inequality a – 2b + 10 > 0 is

Q4

An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5 is then,

Q5

If the papers of 4 students can be checked by any one of the 7 teachers, then the probability that all the 4 papers are checked by exactly 2 teachers is

Q6

Let ABC, be three mutually independent events. Consider the two statements S1 and S2.

                        S1 : A and B ∪ C are independent

                        S2 : A and B ∩ C are independent

Then

Q7

If m is a natural such that m ≤ 5, then the probability that the quadratic that the quadratic equation x2 + mx +  has real roots is

Q8

There are m persons setting in a row. Tow of then the selected at random. The probability that the two selected person are not together is

Q9

The probability that at least one of A and B occurs is 0.6. If A and B occur simultaneously with probability 0.3, then P(A’) + P(B’) is

Q10

If the mean and variance of a binomial variate X are 2 and 1 respectively, then the probability that X takes values at most 3 is