NCERT Solutions for Class 11 Maths Chapter 16 Ex 16.1 | Updated For 2021-22

A coin has two faces: head (H) and tail (T). When a coin is tossed three times, the total number of possible outcomes is 23 = 8 Thus, when a coin is tossed three times, the sample space is given by: S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}

When a die is thrown, the possible outcomes are 1, 2, 3, 4, 5, or 6. When a die is thrown two times, the sample space is given by S = {(x, y): x, y = 1, 2, 3, 4, 5, 6} The number of elements in this sample space is 6 × 6 = 36, while the sample space is given by: 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)}

A die has six faces that are numbered from 1 to 6, with one number on each face. Let us denote the red, white, and blue dices as R, W, and B respectively. Accordingly, when a die is selected and then rolled, the sample space is given by S = {R1, R2, R3, R4, R5, R6, W1, W2, W3, W4, W5, W6, B1, B2, B3, B4, B5, B6}
An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.
A coin has two faces: head (H) and tail (T). A die has six faces that are numbered from 1 to 6, with one number on each face. Thus, in the given experiment, the sample space is given by S = {HH, HT, T1, T2, T3, T4, T5, T6}

In this experiment, six may come up on the first throw, the second throw, the third throw and so on till six is obtained. Hence, the sample space of this experiment is given by S = {6, (1, 6), (2, 6), (3, 6), (4, 6), (5, 6), (1, 1, 6), (1, 2, 6), … , (1, 5, 6), (2, 1, 6), (2, 2, 6), … , (2, 5, 6), … ,(5, 1, 6), (5, 2, 6), …}

When a die is rolled, the sample space is given by S = {1, 2, 3, 4, 5, 6} Accordingly, E = {4} and F = {2, 4, 6} It is observed that E ∩ F = {4} ≠ Φ Therefore, E and F are not mutually exclusive events.