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प्रश्न
Two unbiased dice are thrown. Find the probability that the total of the numbers on the dice is greater than 10.
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उत्तर
If two dices are thrown simultaneously, then all the possible outcomes = 62 = 36
∴ Total number of possible outcome, n(S) = 36
Let A = event where the the total of the numbers on the dices is greater than 10
Then the favourable outcomes are as follows:
A = {(5, 6), (6, 5), (6, 6)}
Number of favourable outcomes, n(A) = 3
Hence, required probability, P(A) = P (total of the numbers on the dices is greater than 10) = \[\frac{3}{36} = \frac{1}{12}\]
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Which of the following can not be valid assignment of probabilities for outcomes of sample space S = {ω1, ω2,ω3,ω4,ω5,ω6,ω7}
| Assignment | ω1 | ω2 | ω3 | ω4 | ω5 | ω6 | ω7 |
| (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` |
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| (ii) |
\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
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\[\frac{1}{7}\]
|
Which of the cannot be valid assignment of probability for elementary events or outcomes of sample space S = {w1, w2, w3, w4, w5, w6, w7}:
| Elementary events: | w1 | w2 | w3 | w4 | w5 | w6 | w7 |
| (iv) |
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\[\frac{2}{14}\]
|
\[\frac{3}{14}\]
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\[\frac{4}{14}\]
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\[\frac{5}{14}\]
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\[\frac{6}{14}\]
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\[\frac{15}{14}\]
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