The probability that a dessert sold at a certain café contains chocolate is 75%. The probability that a dessert contains both chocolate and nuts is 23%. Find the probability that a randomly chosen chocolate dessert contains nuts. Round to the nearest tenth of a percent.
To solve this problem, we need to use the formula for conditional probability:
P(A given B) = P(A and B) / P(B)
In this case, we want to find the probability that a chocolate dessert contains nuts, given that it already contains chocolate. So our event A is "dessert contains nuts" and our event B is "dessert contains chocolate".
We know that P(B) = 0.75, since 75% of the desserts contain chocolate. We also know that P(A and B) = 0.23, since 23% of the desserts contain both chocolate and nuts.
Plugging these values into the formula, we get:
P(A given B) = 0.23 / 0.75 = 0.3067...
Rounded to the nearest tenth of a percent, the probability that a randomly chosen chocolate dessert contains nuts is 30.7%.