The probability that a student passes Physics test is 2/3 and the probability that he passes <strong>BOTH</strong> Physics test and English test is 11/15. The probability that he passes <strong>AT LEAST</strong> one test is 4/5. What is the probability that he passes English test?

Explanation

We are given P(P) = \frac{2}{3}, P(P \cap E) = \frac{11}{15}, and P(P \cup E) = \frac{4}{5}. Using the addition theorem, P(P \cup E) = P(P) + P(E) - P(P \cap E). Substituting the values: \frac{4}{5} = \frac{2}{3} + P(E) - \frac{11}{15}. Rearranging for P(E): P(E) = \frac{4}{5} - \frac{2}{3} + \frac{11}{15} = \frac{12 - 10 + 11}{15} = \frac{13}{15}.

Related questions on Statistics & Probability

• Let x be the mean of squares of first n natural numbers and y be the square of mean of first n natural numbers. If $\frac{x}{y}=\fra...
• What is the probability of getting a composite number in the list of natural numbers from 1 to 50?
• Two numbers x and y are chosen at random from a set of first 10 natural numbers. What is the probability that (x+y) is divisible by 4?
• A number x is chosen at random from first n natural numbers. What is the probability that the number chosen satisfies $x+\frac{1}{x} \gt...
• Three fair dice are tossed once. What is the probability that they show different numbers that are in AP?