Question

Jon loves to bake on Saturday's at home. When there, his two favorite desserts to bake are brownies and snickerdoodles. L A represent the event that he bakes brownies at home on Saturday and B represent the event that he bakes snickerdoodl at home on Saturday. If A and B are independent events with P(A) = 0.10 and P(A AND B) = 0.09, find P(B).

Answer 1

To find the probability that Jon bakes snickerdoodles (P(B)), given that the occurrence of baking brownies and snickerdoodles is independent, we use the formula P(A AND B) = P(A) × P(B). Substituting the given probabilities, we find that P(B) is 0.9, or 90%.

Step-by-step explanation:

The student wants to find the probability of Jon baking snickerdoodles at home on a Saturday, given that the events of baking brownies and snickerdoodles are independent, and that we have the probabilities P(A) = 0.10 and P(A AND B) = 0.09. Since events A and B are independent, the probability of both events occurring is the product of their individual probabilities P(A) × P(B).

To find P(B), we can set up the equation P(A AND B) = P(A) × P(B). We already know that P(A AND B) = 0.09 and P(A) = 0.10. Substituting these values into the equation gives us 0.09 = 0.10 × P(B). Solving for P(B), we get P(B) = 0.09 / 0.10, which simplifies to P(B) = 0.9. Therefore, the probability that Jon bakes snickerdoodles on a Saturday is 0.9, or 90%.