Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

In an experiment, the probability that event AA occurs is 34\frac{3}{4}, the probability that event BB occurs is 67\frac{6}{7}, and the probability that events AA and BB both occur is 914\frac{9}{14}. \newlineAre AA and BB independent events? \newlineChoices: \newline(A) yes \newline(B) no

Full solution

Q. In an experiment, the probability that event AA occurs is 34\frac{3}{4}, the probability that event BB occurs is 67\frac{6}{7}, and the probability that events AA and BB both occur is 914\frac{9}{14}. \newlineAre AA and BB independent events? \newlineChoices: \newline(A) yes \newline(B) no
  1. Calculate individual probabilities: To check if events AA and BB are independent, we need to see if the probability of AA and BB occurring together (P(A and B)P(A \text{ and } B)) is equal to the product of their individual probabilities (P(A)×P(B)P(A) \times P(B)).
  2. Calculate product of probabilities: First, calculate the product of P(A)P(A) and P(B)P(B).P(A)×P(B)=(34)×(67)P(A) \times P(B) = \left(\frac{3}{4}\right) \times \left(\frac{6}{7}\right).
  3. Perform multiplication: Now, do the multiplication.\newline(34)×(67)=1828(\frac{3}{4}) \times (\frac{6}{7}) = \frac{18}{28}.

More problems from Identify independent events