Question

Write sample space ‘S’ and number of sample point n(S) for each of the following experiments. Also write events A, B, C in the set form and write n(A), n(B), n(C).
(1) One die is rolled,
Event A : Even number on the upper face.
Event B : Odd number on the upper face.
Event C : Prime number on the upper face.

(2) Two dice are rolled simultaneously,
Event A : The sum of the digits on upper faces is a multiple of 6.
Event B : The sum of the digits on the upper faces is minimum 10.
Event C : The same digit on both the upper faces.

(3) Three coins are tossed simultaneously.
Condition for event A : To get at least two heads.
Condition for event B : To get no head.
Condition for event C : To get head on the second coin.

(4) Two digit numbers are formed using digits 0, 1, 2, 3, 4, 5 without repetition of the digits.
Condition for event A : The number formed is even
Condition for event B : The number formed is divisible by 3.
Condition for event C : The number formed is greater than 50.

(5) From three men and two women, environment committee of two persons is to be formed.
Condition for event A : There must be at least one woman member.
Condition for event B : One man, one woman committee to be formed.
Condition for event C : There should not be a woman member.

(6) One coin and one die are thrown simultaneously.
Condition for event A : To get head and an odd number.
Condition for event B : To get a head or tail and an even number.
Condition for event C : Number on the upper face is greater than 7 and tail on the coin.

Answer 1

(1) Sample Space = {1, 2, 3, 4, 5, 6}
∴ n(S) = 6
A = {2, 4, 6}
∴ n(A) = 3,
B = {1, 3, 5}
∴ n(B) = 3,
C = {2, 3, 5}
∴ n(C) = 3
(2) $\mathrm{Sample}\mathrm{Space}\left(\mathrm{S}\right)=\left\{\begin{array}{cccccc}\left(1,1\right)& \left(1,2\right)& \left(1,3\right)& \left(1,4\right)& \left(1,5\right)& \left(1,6\right)\\ \left(2,1\right)& \left(2,2\right)& \left(2,3\right)& \left(2,4\right)& \left(2,5\right)& \left(2,6\right)\\ \left(3,1\right)& \left(3,2\right)& \left(3,3\right)& \left(3,4\right)& \left(3,5\right)& \left(3,6\right)\\ \left(4,1\right)& \left(4,2\right)& \left(4,3\right)& \left(4,4\right)& \left(4,5\right)& \left(4,6\right)\\ \left(5,1\right)& \left(5,2\right)& \left(5,3\right)& \left(5,4\right)& \left(5,5\right)& \left(5,6\right)\\ \left(6,1\right)& \left(6,2\right)& \left(6,3\right)& \left(6,4\right)& \left(6,5\right)& \left(6,6\right)\end{array}\right\}$

∴ n(S) = 36
A = {(1, 5) (2, 4) (3, 3) (4, 2) (5, 1) (6, 6)}
∴ n(A) = 6

B = {(4, 6) (5, 5) (5, 6) (6, 4) (6, 5) (6, 6)}
∴ n(B) = 6
C = {(1, 1) (2, 2) (3, 3) (4, 4) (5, 5) (6, 6)}
∴ n(C) = 6

(3) Sample Space (S) = {HHH, HHT, HTT, HTH, THT, TTH, THH, TTT}
∴ n(S) = 8
A = {HHH, HHT, HTH, THH}
∴ n(A) = 4
B = {TTT}
∴ n(B) = 1
C = {HHH, HHT, THH}
∴ n(C) = 3

(4) Sample Space (S) = {10, 12, 13, 14, 15, 20, 21, 23, 24, 25, 30, 31, 32, 34, 35, 40, 41, 42, 43,
45, 50, 51, 52, 53, 54}
∴ n(S) = 25
A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54}
∴ n(A) = 13
B = {12, 15, 21, 24, 30, 42, 45, 51, 54}
∴ n(B) = 9
C = {51, 52, 53, 54}
∴ n(C) = 4

(5) S = {M₁M₂, M₁M₃, M₁F₁, M₁F₂, M₂M₃, M₂F₁, M₂F₂, M₃F₁, M₃F₂, F₁F₂}
∴ n(S) = 10
A = {M₁F₁, M₁F₂, M₂F₁, M₂F₂, M₃F₁, M₃F₂, F₁F₂}
∴ n(A) = 7
B = {M₁F₁, M₁F₂, M₂F₁, M₂F₂, M₃F₁, M₃F₂}
n(B) = 6
C = {M₁M₂, M₁M₃, M₂M₃, }
∴ n(C) = 3


(6) S = {H1, H2, H3, H4, H5, H6 T1, T2, T3, T4, T5, T6}
∴ n(S) = 12
A = {H1, H3, H5}
∴ n(A) = 3
B = {H2, H4, H6, T2, T4, T6}
∴ n(B) = 6
C = {}
∴ n(C) = 0