Ivan attended his town's annual Worm Charming Competition. Contestants are assigned to a square foot of land, where they have 30 minutes to "charm" worms to the surface of the dirt. Ivan observed contestants' charming techniques and kept track of how many worms surfaced.The probability that a contestant tried tapping the ground is 0.3, the probability that a contestant charmed over 30 worms is 0.5, and the probability that a contestant tried tapping the ground and charmed over 30 worms is 0.2.What is the probability that a randomly chosen contestant tried tapping the ground or charmed over 30 worms?Write your answer as a whole number, decimal, or simplified fraction.
Question
Ivan attended his town's annual Worm Charming Competition. Contestants are assigned to a square foot of land, where they have 30 minutes to "charm" worms to the surface of the dirt. Ivan observed contestants' charming techniques and kept track of how many worms surfaced.The probability that a contestant tried tapping the ground is 0.3, the probability that a contestant charmed over 30 worms is 0.5, and the probability that a contestant tried tapping the ground and charmed over 30 worms is 0.2.What is the probability that a randomly chosen contestant tried tapping the ground or charmed over 30 worms?Write your answer as a whole number, decimal, or simplified fraction.
Solution
The probability that a randomly chosen contestant tried tapping the ground or charmed over 30 worms can be found using the formula for the probability of the union of two events: P(A or B) = P(A) + P(B) - P(A and B).
Here, event A is that a contestant tried tapping the ground and event B is that a contestant charmed over 30 worms.
P(A) = 0.3 (probability that a contestant tried tapping the ground) P(B) = 0.5 (probability that a contestant charmed over 30 worms) P(A and B) = 0.2 (probability that a contestant tried tapping the ground and charmed over 30 worms)
Substituting these values into the formula gives:
P(A or B) = P(A) + P(B) - P(A and B) = 0.3 + 0.5 - 0.2 = 0.6
So, the probability that a randomly chosen contestant tried tapping the ground or charmed over 30 worms is 0.6.
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