X can solve 80% of the problems while Y can solve 90% of the problems given in a statistics book.A problem is selected at random. What is the probability that at least one of them will solve thesame?
Question
X can solve 80% of the problems while Y can solve 90% of the problems given in a statistics book.A problem is selected at random. What is the probability that at least one of them will solve thesame?
Solution
To solve this problem, we need to find the probability that at least one of them will solve the problem. This is equivalent to finding the probability that either X solves the problem, or Y solves the problem, or both solve the problem.
Step 1: Find the probability that X solves the problem. This is given as 80%, or 0.8.
Step 2: Find the probability that Y solves the problem. This is given as 90%, or 0.9.
Step 3: Find the probability that both X and Y solve the problem. This is the probability that X solves the problem multiplied by the probability that Y solves the problem, or 0.8 * 0.9 = 0.72.
Step 4: Find the probability that at least one of them solves the problem. This is the sum of the probabilities that X solves the problem and that Y solves the problem, minus the probability that both solve the problem (to avoid double-counting). So, the probability is 0.8 + 0.9 - 0.72 = 0.98, or 98%.
So, the probability that at least one of them will solve the problem is 98%.
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