Exams › JEE Main › Maths
For two arbitrary events M and N, what is the probability that one and only one of them happens?
- P(M)+P(N)-P(M∩N)
- P(M)+P(N)+P(M∩N)
- P(M)+P(N)
- P(M)+P(N)-2 P(M∩N)
Correct answer: P(M)+P(N)-2 P(M∩N)
Solution
'One and only one happens' means (M and not N) or (N and not M). P(M only)=P(M)-P(M∩N) and P(N only)=P(N)-P(M∩N); adding gives P(M)+P(N)-2P(M∩N).
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?
- 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?
- Out of 600 bolts, 20% are oversized and 10% are undersized. The rest are acceptable. If one bolt is chosen at random, what is the probability that it is acceptable?
⚔️ Practice JEE Main Maths free + battle 1v1 →