In an experiment, the probability that event A occurs is 1/7, the probability that event B occurs is 3/4, and the probability that events A and B both occur is 3/28. Are A and B independent events? Choices: (A)yes (B)no

Check Independence Criteria: To check if events A and B are independent, we need to see if the probability of A and B occurring together (P(A and B)) is equal to the product of their individual probabilities (P(A) * P(B)).Calculate Individual Probabilities: First, let's find the product of P(A) and P(B). P(A) * P(B) = (1/7) * (3/4)Calculate Product: Now, calculate the product. (1/7) * (3/4) = 3/28Compare Probabilities: Next, we compare this product to the probability of A and B both occurring, which is given as 3/28.Verify Equality: Since P(A and B) = 3/28 and P(A) * P(B) = 3/28, the probabilities are equal.Conclusion: Therefore, events A and B are independent because the product of their individual probabilities equals the probability of them both occurring.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In an experiment, the probability that event $A$ occurs is $\frac{1}{7}$ , the probability that event $B$ occurs is $\frac{3}{4}$ , and the probability that events $A$ and $B$ both occur is $\frac{3}{28}$ . $\newline$ Are $A$ and $B$ independent events? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

View step-by-step help

Home

Math Problems

Precalculus

Identify independent events

Full solution

Q. In an experiment, the probability that event

A

occurs is

\frac{1}{7}

, the probability that event

B

occurs is

\frac{3}{4}

, and the probability that events

A

and

B

both occur is

\frac{3}{28}

\newline

Are

A

and

B

independent events?

\newline

Choices:

\newline

(A) yes

\newline

(B) no

Check Independence Criteria: To check if events $A$ and $B$ are independent, we need to see if the probability of $A$ and $B$ occurring together ( $P(A \text{ and } B)$ ) is equal to the product of their individual probabilities ( $P(A) \times P(B)$ ).
Calculate Individual Probabilities: First, let's find the product of $P(A)$ and $P(B)$ . $\newline$ $P(A) \times P(B) = \left(\frac{1}{7}\right) \times \left(\frac{3}{4}\right)$
Calculate Product: Now, calculate the product. $\newline$ $(\frac{1}{7}) \times (\frac{3}{4}) = \frac{3}{28}$
Compare Probabilities: Next, we compare this product to the probability of $A$ and $B$ both occurring, which is given as $\frac{3}{28}$ .
Verify Equality: Since $P(A \text{ and } B) = \frac{3}{28}$ and $P(A) \times P(B) = \frac{3}{28}$ , the probabilities are equal.
Conclusion: Therefore, events $A$ and $B$ are independent because the product of their individual probabilities equals the probability of them both occurring.