NCERT Class XI Mathematics - Probability - Solutions
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Question : 24
Total: 54
Which of the following cannot be valid assignment of probabilities for outcomes of sample space S = {ω 1 , ω 2 , ω 3 , ω 4 , ω 5 , ω 6 , ω 7
| Assignment | | | | | | | |
|---|---|---|---|---|---|---|---|
| (a) | 0.1 | 0.01 | 0.05 | 0.03 | 0.01 | 0.2 | 0.6 |
| (b) | 1/7 | 1/7 | 1/7 | 1/7 | 1/7 | 1/7 | 1/7 |
| (c) | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 | 0.7 |
| (d) | - 0.1 | 0.2 | 0.3 | 0.4 | - 0.2 | 0.1 | 0.3 |
| (e) | 1/14 | 2/14 | 3/14 | 4/14 | 5/14 | 6/14 | 15/14 |
Solution:
(a) Sum of probabilities
= 0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6 = 1.00
∴ Assignment of probabilities is valid.
(b) Sum of probabilities
=
+
+
+
+
+
+
∴ Assignment of probabilities is valid.
(c) Sum of probabilities
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 = 2.8
Sum of probabilities is greater than 1.
∴ This assignment of probabilities is not valid.
(d) Probability of any event cannot be negative. Therefore, this assignment of probabilities is not valid.
(e) The last probability
∴ This assignment of probabilities is not valid.
= 0.1 + 0.01 + 0.05 + 0.03 + 0.01 + 0.2 + 0.6 = 1.00
∴ Assignment of probabilities is valid.
(b) Sum of probabilities
=
∴ Assignment of probabilities is valid.
(c) Sum of probabilities
= 0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 = 2.8
Sum of probabilities is greater than 1.
∴ This assignment of probabilities is not valid.
(d) Probability of any event cannot be negative. Therefore, this assignment of probabilities is not valid.
(e) The last probability
∴ This assignment of probabilities is not valid.
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