Question

In Minneapolis, the probability that it will be mostly cloudy is 75% andthe probability that it will rain is 71%.If the probability that it will rain and be mostly cloudy is 85%, thenwhat is the probability that it will be mostly cloudy or it will rain?85%61%81%53%3 of 4 QUESTIONS

Answer 1

Let:

Event A: Rain

Event B: mostly cloudly

Then, the probability (P) of the events occurring is:

P(A) = 0.71

P(B) = 0.75

P(A and B) = 0.85

Since the events are non-mutually exclusive, P(A or B) can be found using the formula below:

$P(A\text{ }or\text{ }B)=P(A)+P(B)-P(A\text{ }and\text{ }B)$

The probability that it will be mostly cloudy or it will rain is P(A or B), substituting the values, we have:

$\begin{gathered} P(A\text{ }or\text{ }B)=71+75-85 \\ P(A\text{ }or\text{ }B)=61percent \end{gathered}$

Answer: 61%.