Question

the probability of a thunderstorm on memorial day 0.72 and the probability of a thunderstorm on independance day is 0.14. assuming that these two events are independent, what is the probability of thunderstorms on both memorial day and independence day

Answer 1

Answer:

0.1008 = 10.08% probability of thunderstorms on both memorial day and independence day.

Step-by-step explanation:

Probability of independent events:

If two events are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:

$P(A \cap B) = P(A)P(B)$

In this question:

Event A: Thunderstorm on memorial day.

Event B: Thunderstorm on memorial day

The probability of a thunderstorm on memorial day 0.72

This means that $P(A) = 0.72$

The probability of a thunderstorm on independance day is 0.14.

This means that $P(B) = 0.14$

What is the probability of thunderstorms on both memorial day and independence day?

$P(A \cap B) = P(A)P(B) = 0.72*0.14 = 0.1008$

0.1008 = 10.08% probability of thunderstorms on both memorial day and independence day.

Answer 2

Probabilities are used to determine the chances of events

The probability of thunderstorm on both days is 0.1008

Represent the event that there is thunderstorm on Memorial Day with A, and the event that there is thunderstorm on Independence Day with B

So, we have:

P(A) = 0.72

P(B) = 0.14

The probability of thunderstorm on both days is then calculated as;

P(Both) = P(A) * P(B) - P(A or B)

Given that the events are independent, the equation becomes

P(Both) = P(A) * P(B)

So, we have:

P(Both) = 0.72 * 0.14

Multiply

P(Both) = 0.1008

Hence, the probability of thunderstorm on both days is 0.1008

Read more about probabilities at:

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