Answer:
0.25 = 25% probability that it will rain today and ruin your picnic
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event A: Cloudy skies
Event B: Rain
20% of all days start with clouds in the air
This means that [tex]P(A) = 0.2[/tex]
50% of rainy days start with rain clouds in the air
50% of 10%. So
[tex]P(A \cap B) = 0.5*0.1 = 0.05[/tex]
What is the probability that it will rain today and ruin your picnic
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.05}{0.2} = 0.25[/tex]
0.25 = 25% probability that it will rain today and ruin your picnic
