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`        A coin is tossed. If head comes up ,apair of die is thrown and sum obtained is noted. If tails comes up ,a card from 1 to 9 is chosen, and chosen number is noted . Find probability that number noted is 7 or 8`
one year ago

```							Please find the answer to your questionE1 ≡ number noted is 7, E2 ≡ number notes is 8,H ≡ getting head on coin, T ≡ getting tail on coin.Then by total probability theorem,P (E1) = P (H) P (E1| H) + P (T) P (E1| T)And P (E2) = P (H) P (E2| H) + P (T) P (E2| T)Where P (H) = 1/2 ; P (T) = 1/2P (E1| H) = prob. of getting a sum of 7 on two dice. Here favorable cases are{(1, 6), (6, 1), (2, 5), (5, 2), (3, 4), (4, 3)}∴ P (E1| H) = 6/36 = 1/6Also P (E1| T) = prob. if getting ‘7’ numbered card out of 11 cards = 1/11.P (E2| H) = Prob. of getting a sum of 8 on two dice. Here favorable cases are{(2, 6), (6, 2), (4, 4), (5, 3), (3, 5)}∴ P (E2| H) = 5/36P (E2| T) = prob. of getting ‘8’ numbered card out of 11 cards = 1/11∴ P (E1) = 1/2 x 1/6 + 1/2 x 1/11 = 1/12 + 1/22 = 11 + 6/132 = 17/132P (E2) = 1/2 x 5/36 + 1/2 x 1/11 = 1/2 [55 + 36/396] = 91/792Now E1 and E2 are mutually exclusive events thereforeP (E1 or E2) = P (E1) + P (E2) = 17/132 + 91/792= 102 + 91/792 = 193/792 = 0.2436
```
one year ago
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