Marshall entered his sister into their town's Smelly Shoe Competition. Marshall observed contestants of all ages proudly strutting around wearing different kinds of smelly shoes.The probability that a contestant is under age 12 is 0.2, the probability that a contestant is wearing tennis shoes is 0.2, and the probability that a contestant is under age 12 or is wearing tennis shoes is 0.3.What is the probability that a randomly chosen contestant is under age 12 and is wearing tennis shoes?Write your answer as a whole number, decimal, or simplified fraction
Question
Marshall entered his sister into their town's Smelly Shoe Competition. Marshall observed contestants of all ages proudly strutting around wearing different kinds of smelly shoes.The probability that a contestant is under age 12 is 0.2, the probability that a contestant is wearing tennis shoes is 0.2, and the probability that a contestant is under age 12 or is wearing tennis shoes is 0.3.What is the probability that a randomly chosen contestant is under age 12 and is wearing tennis shoes?Write your answer as a whole number, decimal, or simplified fraction
Solution
To find the probability that a contestant is under age 12 and is wearing tennis shoes, we can use the formula for the probability of the union of two events:
P(A or B) = P(A) + P(B) - P(A and B)
We know that:
P(A) = Probability that a contestant is under age 12 = 0.2 P(B) = Probability that a contestant is wearing tennis shoes = 0.2 P(A or B) = Probability that a contestant is under age 12 or is wearing tennis shoes = 0.3
We can substitute these values into the formula to find P(A and B):
0.3 = 0.2 + 0.2 - P(A and B)
Solving for P(A and B) gives:
P(A and B) = 0.2 + 0.2 - 0.3 = 0.1
So, the probability that a randomly chosen contestant is under age 12 and is wearing tennis shoes is 0.1 or 10%.
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