If P(A)=1/3, P(B)=1/2 and P(A \cap B)=1/4, then what is the value of P(\overline{A} \cup B)?

Explanation

We need P(\overline{A} \cup B) = P(\overline{A}) + P(B) - P(\overline{A} \cap B). We know P(\overline{A}) = 1 - P(A) = 1 - 1/3 = 2/3. Also, P(\overline{A} \cap B) = P(B) - P(A \cap B) = 1/2 - 1/4 = 1/4. Thus, P(\overline{A} \cup B) = 2/3 + 1/2 - 1/4 = 8/12 + 6/12 - 3/12 = 11/12.

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?