QUESTION 2
Easy
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
1
(i) Rolling a die and tossing a coin together
Outcomes of rolling a die : \(\{1, 2, 3, 4, 5, 6\}\)
Outcomes of tossing a coin : \(\{H, T\}\)
Since each die number can occur with either Heads or Tails, combining the outcomes we get
\(S = \{(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)\}\)
Outcomes of tossing a coin : \(\{H, T\}\)
Since each die number can occur with either Heads or Tails, combining the outcomes we get
\(S = \{(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)\}\)
2
(ii) Choosing a random integer between −5 and +5
The integers from −5 to +5 are \(\{−5,−4,−3,−2,−1, 0, 1, 2, 3, 4, 5\}\), so
\(S = \{−5,−4,−3,−2,−1, 0, 1, 2, 3, 4, 5\}\)
\(S = \{−5,−4,−3,−2,−1, 0, 1, 2, 3, 4, 5\}\)
3
(iii) A box containing 5 green and 7 red balls. One ball is drawn at random
Since only the colour matters, the possible outcomes are green ball and red ball. So
\(S = \{Green, Red\}\)
\(S = \{Green, Red\}\)
🏆
Final Answer :
(i) \(S = \{(1,H),(1,T),(2,H),(2,T),(3,H),(3,T),(4,H),(4,T),(5,H),(5,T),(6,H),(6,T)\}\)
(ii) \(S = \{−5,−4,−3,−2,−1, 0, 1, 2, 3, 4, 5\}\)
(iii) \(S = \{Green, Red\}\)
Concept Note
The sample space is the set of all possible outcomes of an experiment.