## 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?

1. sauravshakya

P(thursday and friday of the same week are wet days/Wednesday is dry) =(1-0.6)*0.8

2. sauravshakya

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

how did u solve for a?

4. sauravshakya

It is a conditional probability. And the given condition is that Wedenesday is wet.

5. sauravshakya

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

which formula did you use like P(A/B)=P(A intersection B)/P(B) isnt this the formula for conditional probability?

7. sauravshakya

Yes but not in this case.

8. sauravshakya

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

got it?

10. ash1213

yes !!Thanks !! n wat abt part c?

11. sauravshakya

Isnt it (1-0.6)*(1-0.8)*44

12. ash1213

13. sauravshakya

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

ok thanks

15. sauravshakya

welcome