Q1. When a single 6-sided die is rolled, what is the total number of possible outcomes in the sample space?

Answer:

When a standard 6-sided die is rolled, the possible outcomes are

Sample Space : S= {1, 2, 3, 4, 5, 6}.

Since there are 6 distinct faces on the die.

 Therefore, the total number of possible outcomes in the sample space is 6.

Q2. For the following experiments write down the sample space S. (i) Rolling a die and tossing a coin together.

Answer:

When a die and a coin are rolled and tossed simultaneously, the total number of possible outcomes is the product of the die's outcomes (1–6) and the coin's outcomes (H, T). Thus, each outcome is represented as a pair, with the first element being the die result and the second being the coin result.

The sample space S = {(1,H), (1,T), (2,H), (2,T), (3,H), (3,T), (4,H), (4,T), (5,H),(5,T), (6,H), (6,T)}.

There are 12 outcomes in total.

Q2. (ii) Choosing a random integer between – 5 and + 5.

Answer:

The sample space consists of all the whole numbers located strictly between -5 and +5 are:

Sample Space: (S)= {-4, -3, -2, -1, 0, 1, 2, 3, 4}

So,the sample space contains 9 outcomes.

Method 2

All integers between -5 and +5(including both) are:

Sample Space :(S)= {-5,-4, -3, -2, -1, 0, 1, 2, 3, 4,5}

Thus,the sample space contains 11 outcomes.

Q2. (iii) A box containing 5 green and 7 red balls. One ball is drawn at random.

Answer:

A box containing 5 green and 7 red balls.

one ball is drawn at random .

The Sample space: (S)= {G₁, G₂, G₃, G₄, G₅, R₁, R₂, R₃, R₄, R₅, R₆, R₇}

So,there are 12 possible outcomes.

Q3. 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.'

Answer:

(i) To find the sample space, we pair each snack with every possible drink.

There are 3 snacks: {Samosa ,Pakora ,Bhaji}

There are 2 drinks: {Chai,Lassi} 

Sample space S = {(Samosa-Chai), (Samosa-Lassi), (Pakora-Chai), (Pakora-Lassi), (Bhaji-Chai), (Bhaji-Lassi)}

Therefore, Number of all possible outcomes: 6

(ii) Event: Selecting Samosa as a snack

In this case, the event includes all outcomes where the snack is a Samosa.
Event (E):  E (Selecting Samosa) = {Samosa-Chai, Samosa-Lassi}.
Number of favourable outcomes: 2

Thus ,the event contains 2 favourable outcomes.