Exercise Set 7.3
1. When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?
Solution:
When a single 6-sided die is rolled, the possible outcomes are: 1, 2, 3, 4, 5, 6
So, the sample space, S= {1, 2, 3, 4, 5, 6}
Total number of possible outcomes, n(S) = 6
2. For the following experiments write down the sample space S.
(i) Rolling a die and tossing a coin together.
(ii) Choosing a random integer between – 5 and + 5.
(iii) A box containing 5 green and 7 red balls. One ball is drawn at random.
Solution:
(i) Experiment: Rolling a die and tossing a coin together
The possible outcomes of a die are: {1,2,3,4,5,6}
The possible outcomes of a coin are: {H,T}
Therefore, the sample space is:
S = {(1,H), (2,H), (3,H), (4,H), (5,H), (6,H), (1,T), (2,T), (3,T), (4,T), (5,T), (6,T)}
(ii) Experiment: Choosing a random integer between -5 and +5
Sample space: S = {-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
(iii) Experiment: A box containing 5 green and 7 red balls. One ball is drawn at random.
Since we can either get a green ball or a red ball
So, the sample space is:
S= {Green, Red}
3. In a village fair, there are 3 popular snacks available: Samosa, Pakora, and Bhaji. For drinks, villagers can choose either Chai or Lassi.
(i) List the sample space of all possible snack and drink combinations a person could choose at the fair.
(ii) List the event ‘Selecting Samosa as a snack.’
Solutions:
The available snacks are: Samosa, Pakora, and Bhaji
The available drinks are: Chai, Lassi
(i) Experiment: All possible snack and drink combinations.
Sample space: S = {(Samosa, Chai),(Samosa, Lassi),(Pakora, Chai),(Pakora, Lassi),(Bhaji, Chai),(Bhaji, Lassi)}
(ii) Event: Selecting Samosa as a snack.
E = {(Samosa, Chai),(Samosa, Lassi)}