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ash1213

  • 2 years ago

If a given day is wet, the probability that the following day will also be wet is 0.8. If a given day is dry the probability that the following day will be dry is 0.6. Given that wednesday of a partciular week is dry work out the following; a)thursday and friday of the same week are wet days b)friday of the same week is a wet day c) In one season there were 44 cricket matches, each played over three consecutive days, in which the first and third days were dry. For how many of these matches would you expect the second day was wet?

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  1. sauravshakya
    • 2 years ago
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    P(thursday and friday of the same week are wet days/Wednesday is dry) =(1-0.6)*0.8

  2. sauravshakya
    • 2 years ago
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    P(friday of the same week is a wet day/Wednesday is dry) =0.6 * (1-0.6) + (1-0.6)*0.8

  3. ash1213
    • 2 years ago
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    how did u solve for a?

  4. sauravshakya
    • 2 years ago
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    It is a conditional probability. And the given condition is that Wedenesday is wet.

  5. sauravshakya
    • 2 years ago
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    So, the probability that Thursday will be wet is (1-0.6) And if Thursday will be wet the probability Friday will also be wet is 0.8. S0, for (a) it is (1-06)*0.8

  6. ash1213
    • 2 years ago
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    which formula did you use like P(A/B)=P(A intersection B)/P(B) isnt this the formula for conditional probability?

  7. sauravshakya
    • 2 years ago
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    Yes but not in this case.

  8. sauravshakya
    • 2 years ago
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    Because we are given: P(next day is dry/today is dry)=0.6 P(next day is wet/today is wet)=0.8

  9. sauravshakya
    • 2 years ago
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    got it?

  10. ash1213
    • 2 years ago
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    yes !!Thanks !! n wat abt part c?

  11. sauravshakya
    • 2 years ago
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    Isnt it (1-0.6)*(1-0.8)*44

  12. ash1213
    • 2 years ago
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    answer is 8

  13. sauravshakya
    • 2 years ago
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    It is ( Dry,Wet, Dry)/{(Dry,Dry,Dry) + (Dry, Wet , Dry))} *44 1*(1-0.6) * (1-0.8)/{(1*0.6*0.6) + (1* (1-0.6) * (1-0.8) }*44 =8

  14. ash1213
    • 2 years ago
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    ok thanks

  15. sauravshakya
    • 2 years ago
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    welcome

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