Question

1) A single die is rolled twice. The set of 36 equally likely outcomes is {(1, 1), (1, 2), (1, 3), (1, 4), (1,
5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4,
3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6),}.
Find the probability of getting two numbers whose sum is less than 13

a) 1/4 b) 1 c)0 d)1/2

2) six students, A, B, C, D, E, F, are to give speeches to the class. The order of speaking is
determined by random selection. Find the probability that (a) E will speak first (b) that C will
speak fifth and B will speak last (c) that the students will speak in the following order: DECABF
(d) that A or B will speak first.

3) In how many distinct ways can a 11-digit number be made using two 9's and nine 2's?

A)11 B)16 C)8 D)55

Answer 1

Ans:

1) probability of getting two numbers whose sum is less than 13

n=36

total number of oservation having sum less than 13 =36

probability of getting two numbers whose sum is less than 13=36/36=1

Ans)

2) There are 6!=720 permutations of letters :

a)Prob of E will speak firs =1/6

(b) that C will speak fifth and B will speak last =1/24

c) prob that the students will speak in the following order: DECABF =1/720

d)prob that A or B will speak first=1/3

Ans 3)11