Question

if the probability of rain is 0.6, the probability of fog is 0.4, and the probability of rain and fog is 0.1, what is the probability of rain or fog?

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the three - way principle

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the probability of rain or fog is

(type a decimal rounded to two decimal places.)

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Explanation:

Step1: Recall the formula for \(P(A\cup B)\)

The formula for the probability of the union of two events \(A\) and \(B\) is \(P(A\cup B)=P(A)+P(B)-P(A\cap B)\). Let \(A\) be the event of rain and \(B\) be the event of fog. We are given \(P(A) = 0.6\), \(P(B)=0.4\), and \(P(A\cap B)=0.1\).

Step2: Substitute the values into the formula

Substitute the values into the formula: \(P(A\cup B)=0.6 + 0.4-0.1\).

Step3: Calculate the result

\(P(A\cup B)=0.6+0.4 - 0.1=0.9\)

Answer:

\(0.9\)