Question

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?

Answer 1

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

Answer 2

P(friday of the same week is a wet day/Wednesday is dry)
=0.6 * (1-0.6) + (1-0.6)*0.8

Answer 3

how did u solve for a?

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

Yes but not in this case.

Answer 8

Because we are given:
P(next day is dry/today is dry)=0.6
P(next day is wet/today is wet)=0.8

Answer 9

got it?

Answer 10

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

Answer 11

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

Answer 12

answer is 8

Answer 13

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

Answer 14

ok thanks

Answer 15

welcome