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प्रश्न
The accompanying Venn diagram shows three events, A, B, and C, and also the probabilities of the various intersections (for instance, P(A ∩ B) = .07). Determine P(A ∪ B)
उत्तर
From the given Venn diagram
P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= 0.13 + 0.07 + 0.07 + 0.10 + 0.15 – 0.07
= 0.13 + 0.07 + 0.10 + 0.15
= 0.45
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संबंधित प्रश्न
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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| (iii) | 0.7 | 0.06 | 0.05 | 0.04 | 0.03 | 0.2 | 0.1 |
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}:
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| (iv) |
\[\frac{1}{14}\]
|
\[\frac{2}{14}\]
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\[\frac{3}{14}\]
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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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