Two events, A and B, are independent. If [tex]P(A)=0.3[/tex] and [tex]P(B)=0.2[/tex], what is [tex]P(A[/tex] and B)?

Independent events: P ( A and B ) = P ( A ) × P ( B ) .
Substitute given values: P ( A ) = 0.3 and P ( B ) = 0.2 .
Calculate the product: 0.3 × 0.2 = 0.06 .
The probability of both events occurring is: 0.06 ​ .

Explanation

Understand the problem and provided data We are given two independent events, A and B, with their respective probabilities: P ( A ) = 0.3 and P ( B ) = 0.2 . Our goal is to find the probability of both events A and B occurring, which is denoted as P ( A and B ) .

Apply the formula for independent events Since events A and B are independent, the probability of both events occurring is simply the product of their individual probabilities. This is expressed as: P ( A and B ) = P ( A ) × P ( B )

Substitute the given values Now, we substitute the given probabilities into the formula: P ( A and B ) = 0.3 × 0.2

Calculate the final probability Performing the multiplication, we get: P ( A and B ) = 0.06 Therefore, the probability of both events A and B occurring is 0.06.


Examples
In a game, if the probability of winning a prize is 0.3 and the probability of getting a bonus is 0.2, and these events are independent, then the probability of winning a prize and getting a bonus is 0.06. This means that out of 100 games, you would expect to win a prize and get a bonus in 6 of them.

Answered by GinnyAnswer | 2025-07-05

The probability of both independent events A and B occurring is calculated using the formula P ( A and B ) = P ( A ) × P ( B ) . Given P ( A ) = 0.3 and P ( B ) = 0.2 , the result is 0.06 or 6%. This indicates a 6% chance of both events occurring simultaneously.
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Answered by Anonymous | 2025-08-23