In an experiment, the probability that event A occurs is 1/7, the probability that event B occurs is 5/8, and the probability that events A and B both occur is 5/56. 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 Product of Probabilities: First, calculate the product of P(A) and P(B). P(A) * P(B) = (1/7) * (5/8)Multiply Probabilities: Now, do the multiplication. (1/7) * (5/8) = 5/56Compare Probabilities: Next, compare this product to the given probability of A and B occurring together, which is 5/56.Confirm Independence: Since P(A and B) = 5/56 and P(A) * P(B) = 5/56, the probabilities are equal.Therefore, events A and B are independent because the product of their individual probabilities equals the probability of them occurring together.

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In an experiment, the probability that event $A$ occurs is $\frac{1}{7}$ , the probability that event $B$ occurs is $\frac{5}{8}$ , and the probability that events $A$ and $B$ both occur is $\frac{5}{56}$ . $\newline$ Are $A$ and $B$ independent events? $\newline$ Choices: $\newline$ (A) yes $\newline$ (B) no

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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{5}{8}

, and the probability that events

A

and

B

both occur is

\frac{5}{56}

\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 Product of Probabilities: First, calculate the product of $P(A)$ and $P(B)$ . $\newline$ $P(A) \times P(B) = \frac{1}{7} \times \frac{5}{8}$
Multiply Probabilities: Now, do the multiplication. $\newline$ $(\frac{1}{7}) \times (\frac{5}{8}) = \frac{5}{56}$
Compare Probabilities: Next, compare this product to the given probability of $A$ and $B$ occurring together, which is $\frac{5}{56}$ .
Confirm Independence: Since $P(A \text{ and } B) = \frac{5}{56}$ and $P(A) \times P(B) = \frac{5}{56}$ , the probabilities are equal.
Confirm Independence: Since $P(A \text{ and } B) = \frac{5}{56}$ and $P(A) \times P(B) = \frac{5}{56}$ , the probabilities are equal.Therefore, events $A$ and $B$ are independent because the product of their individual probabilities equals the probability of them occurring together.