Question

Suppose there is a 20% chance of rain on Monday and a 40% chance of rain on Tuesday. Assuming the weather on successive days is independent, find

a. the probability it rains on Monday or Tuesday.
b. the conditional probability it rains on Tuesday given that it rained on Monday.

Answer 1

a. 52%

b. 40%

Explanation:

Let A represents the event of raining on Monday and B represents the event of raining in Tuesday,

Then according to the question,

P(A) = 20% = 0.2,

P(B) = 40% = 0.4,

Here, A and B are independent events,

So, P(A∩B) = P(A) × P(B),

⇒ P(A∩B) = 0.2 × 0.4 = 0.08

We know that,

P(A∪B) = P(A) + P(B) - P(A∩B)

a. The probability it rains on Monday or Tuesday, P(A∪B) = 0.2 + 0.4 - 0.08

= 0.52

= 52%

b. The conditional probability it rains on Tuesday given that it rained on Monday,

`P((B)/(A))=(P(A\cap B))/(P(A)) = (0.08)/(0.2)=0.4 = 40\%`