The probability that a dessert sold at a certain cafe contains chocolate is 73%. The probability that a dessert contains both chocolate and nuts is 25%. Find the probability that a randomly chosen chocolate dessert contains nuts. Round to the nearest tenth of a percent.
A. 29.2%
B. 48.0%
C. 34.2%
D. 36%
To find the probability that a randomly chosen chocolate dessert contains nuts, we can use the formula for conditional probability:
P(A|B) = P(A and B) / P(B)
Where:
P(A|B) is the probability of A given B
P(A and B) is the probability of A and B occurring
P(B) is the probability of B occurring
In this case:
A = dessert contains nuts
B = dessert contains chocolate
P(A and B) = 25%
P(B) = 73%
Now we can plug in the values and calculate:
P(A|B) = 25% / 73%
P(A|B) = 0.342
Therefore, the probability that a randomly chosen chocolate dessert contains nuts is approximately 34.2%, so the answer is C. 34.2%.