Home › JEE Main › Mathematics › Statistics and Probability › For any two events A and B, the probability that…
For any two events A and B, the probability that neither occurs always equals:
A1 - P(A and B)
BP(A') + P(B')
CP(A or B) - 1
D1 - P(A or B)
Answer & Solution
Correct answer: D. 1 - P(A or B)
1. Neither A nor B means the outcome lies outside A and outside B.
2. That region is exactly the complement of the union A-or-B.
3. So P(neither) = 1 - P(A or B) for every pair of events.
_Source: NCERT Class 11 Mathematics, Ch 14 'Probability' (kemh114)_
Related questions
For two events, P(A) = 0.54, P(B) = 0.69 and P(A and B) = 0.35. The probability that A occTwo dice are thrown. The probability that the sum of the numbers is at most 4 is:A fair coin is tossed three times. The probability of getting exactly two heads is:One card is drawn from a pack of 52. The probability that it is a red king is:A and B are mutually exclusive, P(not A) = 0.65 and P(A or B) = 0.85. Then P(B) equals:A fair coin is tossed three times. The probability of getting at least one head is:A, B and C are mutually exclusive and exhaustive with P(A) = 1/2 and P(B) = 1/3. Then P(C)One card is drawn from a pack of 52. The probability that it is neither a king nor a queen