On Friday, a meteorologist makes the following forecast. • There’s a 30% chance

Question

On Friday, a meteorologist makes the following forecast.

• There’s a 30% chance of rain on Saturday.

• If it rains on Saturday, then there’s an 80% chance of rain on Sunday.

• If it does not rain on Saturday, then there’s a 10% chance of rain on Sunday.

• It is rains on Saturday and Sunday, then there’s a 60% chance of rain on Monday.

• Otherwise, there’s a 15% chance of rain on Monday.

(a) Find the probability that it rains on Saturday, Sunday, and Monday. (b) Find the probability that it rains on at least one of the three days. (c) Find the probability that it does not rain on Monday.

Explanation / Answer

Ans:

a)P(saturday)=0.3

P(sunday/saturday)=0.8

P(sat and sunday)/P(saturday)=0.8

P(sat and sunday)=0.8*0.3=0.24

P(Suday/not saturday)=0.1

P(Monday/sat and sunday)=0.6

P(monday/not saturday and not sunday)=0.15

a)P(Monday and saturday and sunday)/P(sat and sunday)=0.6

P(monday and saturday and sunday)=0.6*0.24=0.144

c)P(Monday)=P(monday/sat and sunday)*P(saturday and sunday)+P(monday/not sat and not sunday)

=0.6*0.24+0.15*0.76

=0.144+0.114

=0.258

P(not monday)=1-0.258=0.742

b)P(atleast one day)=1-P(none day)

P(not monday/not sat and sunday)=1-0.15=0.85

P(not monday and not sat and not sunday)=0.85*0.76=0.646

P(atleast one day)=1-0.646=0.354

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