Exams › JEE Main › Maths

Let A, B and C be events with P(A) = 0.3, P(B) = 0.4, P(C) = 0.8, P(A ∩ B) = 0.08, P(A ∩ C) = 0.28 and P(A ∩ B ∩ C) = 0.09. If P(A ∪ B ∪ C) is at least 0.75, then

1. 0.23 ≤ P(B ∩ C) ≤ 0.48
2. 0.45 ≤ P(B ∩ C) ≤ 0.75
3. 0.48 ≤ P(B ∩ C) ≤ 0.75
4. None of these.

Correct answer: 0.23 ≤ P(B ∩ C) ≤ 0.48

Solution

P(AUBUC)=PA+PB+PC-P(AB)-P(AC)-P(BC)+P(ABC)=1.23-P(BC). Requiring this ≥0.75 gives P(BC)≤0.48, and requiring it ≤1 gives P(BC)≥0.23, so 0.23 ≤ P(B∩C) ≤ 0.48.

Related JEE Main Maths questions

• A random variable can assume the values 0, 1, 2,..., n, and its corresponding frequencies are proportional to the coefficients nC0, nC1, nC2,..., nCn. What is the variance of this distribution?
• From the integers 1, 2, 3,..., 2004, two distinct numbers x and y are selected at random without replacement. What is the probability that x³ + y³ is divisible by 3?
• One card is selected at random from a standard deck of 52 cards. A player wagers that the card will be a spade or an ace. What are the odds against the player winning the wager?
• When n objects are assigned randomly to n people, what is the probability that at least one person receives no object?
• For two arbitrary events M and N, what is the probability that one and only one of them happens?
• A four-digit number is made using the digits 1, 2, 3, and 4 without repeating any digit. What is the probability that the resulting number is odd?

⚔️ Practice JEE Main Maths free + battle 1v1 →