Maharashtra Board Class 10 Maths Chapter 5 Probability Set 5.3 Solutions

Question 1. Write sample space 'S' and number of sample points 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).
(i) 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.
(ii) 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.
(iii) 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.
(iv) 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 is divisible by 3.
Condition for event C: The number formed is greater than 50.
(v) 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.
(vi) 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:
Solution:
(i) Sample space (S) = {1, 2, 3, 4, 5, 6}
.. n(S) = 6
Condition for event A: Even number on the upper face.
.. A = {2,4,6}
.. n(A) = 3
Condition for event B: Odd number on the upper face.
.. B = {1, 3, 5}
.. n(B) = 3
Condition for event C: Prime number on the upper face.
.. C = {2, 3, 5}
.. n(C) = 3
(ii) Sample space,
S = {(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)}
.. n(S) = 36
Condition for event A: The sum of the digits on the upper faces is a multiple of 6.
A = {(1, 5), (2, 4), (3, 3), (4, 2), (5, 1), (6, 6)}
.. n(A) = 6
Condition for event B: The sum of the digits on the upper faces is minimum 10.
B = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
.. n(B) = 6
Condition for event C: The same digit on both the upper faces.
C = {(1, 1), (2, 2), (3, 3), (4, 4), (5, 5), (6, 6)}
.. n(C) = 6
(iii) Sample space,
S = {HHH, HHT, ΗΤΗ, ΤΗΗ, HTT, THT, TTH, TTT}
.. n(S) = 8
Condition for event A: To get at least two heads.
.. A = {HHT, HTH, THH, HHH}
.. n(A) = 4
Condition for event B: To get no head.
.. B = {TTT}
.. n(B) = 1
Condition for event C: To get head on the second coin.
.. C = {HHH, HHT, THH, THT}
.. n(C) = 4
(iv) 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
Condition for event A: The number formed is even
.. A = {10, 12, 14, 20, 24, 30, 32, 34, 40, 42, 50, 52, 54)
.. n(A) = 13
Condition for event B: The number formed is divisible by 3.
.. B = {12, 15, 21, 24, 30, 42, 45, 51, 54}
.. n(B) = 9
Condition for event C: The number formed is greater than 50.
.. C = {51,52, 53,54}
.. n(C) = 4
(v) Let the three men be M1, M2, M3 and the two women be W1, W2.
Out of these men and women, a environment committee of two persons is to be formed.
.. Sample space,
S = {M1M2, M1M3, M₁W1, M1W2, M2M3, M2W1, M2W2, M3W1, M3W2, W1W2}
.. n(S) = 10
Condition for event A: There must be at least one woman member.
.. A = {M₁W1, M1W2, M2W1, M2W2, M3W1, M3W2, W1W2}
.. n(A) = 7
Condition for event B: One man, one woman committee to be formed.
.. B = {M₁W1, M1W2, M2W1, M2W2, M3W2, M3W2}
.. n(B) = 6
Condition for event C: There should not be a woman member.
.. C = {M₁M2, M1M3, M2M3}
.. n(C) = 3
(vi) Sample space,
S = {(H, 1), (H, 2), (H, 3), (Η, 4), (Η, 5), (Η, 6), (Τ, 1), (Τ, 2), (Τ, 3), (Τ, 4), (Τ, 5), (Τ, 6)}
.. n(S) = 12
Condition for event A: To get head and an odd number.
.. A = {(H, 1), (Η, 3), (Η, 5)}
.. n(A) = 3
Condition for event B: To get a head or tail and an even number.
.. B = {(H, 2), (Η, 4), (Η, 6), (T, 2), (T, 4), (T, 6)}
.. n(B) = 6
Condition for event C: Number on the upper face is greater than 7 and tail on the coin.
The greatest number on the upper face of a die is 6.
.. Event C is an impossible event.
.. C = { }
.. n(C) = 0
In simple words: This question requires identifying all possible outcomes (sample space S) and their total count (n(S)) for various experiments, then defining specific events (A, B, C) within that sample space and counting their respective outcomes (n(A), n(B), n(C)). It tests the fundamental understanding of probability definitions.

🎯 Exam Tip: Accurately listing all elements of the sample space and then carefully filtering for each event is crucial for scoring. Pay close attention to conditions like "at least two," "minimum," "without repetition," and "impossible event" to avoid errors.