Question

NO LINKS!! Please help me with this probability question​

Answer 1

b) About 46.67%.

Explanation:

Let event A = being cloudy.

Let even B = being rainy.

Given probabilities:

• Probability of being cloudy = 30%.
• Probability of being rainy = 15%.
• Probability of being cloudy and rainy = 14%.

Therefore:

• P(A) = 0.3
• P(B) = 0.15
• P(A ∩ B) = 0.14

Conditional Probability Formula

`\sf P(B|A)=(P(A \cap B))/(P(A))`

The probability of being rainy given it is cloudy = P(B | A).

Substitute the given values into the formula:

`\implies \sf P(B|A)=(0.14)/(0.3)=0.46666...=46.67\%\;(2\;d.p.)`

Therefore, the probability of it being rainy if you know it will be cloudy is about 46.67%.

Answer 2

Answer: B) 46.67% approximately

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Work Shown:

A = it will be cloudy tomorrow

B = it will be rainy tomorrow

P(A) = 0.30

P(B) = 0.15

P(A and B) = 0.14

Apply the conditional probability formula.

P(B given A) = P(A and B)/P(A)

P(B given A) = 0.14/0.30

P(B given A) = 0.4667 approximately

P(B given A) = 46.67% approximately