As per the prediction of weather bureau, the probabilities for rains o

1.	As per the prediction of weather bureau, the probabilities for rains on three days; Thursday, Friday and Saturday in the next week are 0.8, 0.7 and 0.6 respectively. Find the probability that it rains on at least one of the three days in the next week.(Note:The events of rains on three days; Thursday, Friday and Saturday of a week are independent.)
Answer» A = Event that it rains on Thursday B = Event that it rains on Friday C = Event that it rains on Saturday Here, P(A) = 0.8, P(B) = 0.7 and P(C) = 0.6 are given. A, B and C are independent events. ∴ P(A ∩B) = P(A) ∙ P(B) = 0.8 × 0.7 = 0.56 P(A ∩ C) = P(A) ∙ P(C) = 0.8 × 0.6 = 0.48 P(B ∩ C) = P(B) ∙ P(C) = 0.7 × 0.6 = 0.42 P(A ∩ B ∩ C) = P(A) ∙ P(B) ∙ P(C) = 0.8 × 0.7 × 0.6 = 0.336 Now, A ∪ B ∪ C = Event that it rains on at least one of the three days in the next week According to the law of addition of probability, P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(A ∩ C) – P(B ∩ C) + P(A ∩ B ∩ C) = 0.8 + 0.7 + 0.6 – 0.56 – 0.48 – 0.42 + 0.336 = 0.976

As per the prediction of weather bureau, the probabilities for rains on three days; Thursday, Friday and Saturday in the next week are 0.8, 0.7 and 0.6 respectively. Find the probability that it rains on at least one of the three days in the next week.(Note:The events of rains on three days; Thursday, Friday and Saturday of a week are independent.)

Answer»

A = Event that it rains on Thursday
B = Event that it rains on Friday
C = Event that it rains on Saturday

Here, P(A) = 0.8, P(B) = 0.7 and P(C) = 0.6 are given.
A, B and C are independent events.

∴ P(A ∩B) = P(A) ∙ P(B) = 0.8 × 0.7 = 0.56

P(A ∩ C) = P(A) ∙ P(C) = 0.8 × 0.6 = 0.48

P(B ∩ C) = P(B) ∙ P(C) = 0.7 × 0.6 = 0.42

P(A ∩ B ∩ C) = P(A) ∙ P(B) ∙ P(C)

= 0.8 × 0.7 × 0.6 = 0.336

Now, A ∪ B ∪ C = Event that it rains on at least one of the three days in the next week

According to the law of addition of probability,

P(A ∪ B ∪ C) = P(A) + P(B) + P(C) – P(A ∩ B) – P(A ∩ C) –

P(B ∩ C) + P(A ∩ B ∩ C)

= 0.8 + 0.7 + 0.6 – 0.56 – 0.48 – 0.42 + 0.336

= 0.976