Advertisements
Advertisements
प्रश्न
If A and B are two events associated with a random experiment such that P(A) = 0.3, P (B) = 0.4 and P (A ∪ B) = 0.5, find P (A ∩ B).
Advertisements
उत्तर
Given:
P(A) = 0.3, P (B) = 0.4 and P (A ∪ B) = 0.5
By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
⇒ 0.5 = 0.3 + 0.4 -P (A ∩ B)
⇒ 0.5 = 0.7 - P (A ∩ B)
⇒ P (A ∩ B) = 0.7 - 0.5
= 0.2
Hence, P (A ∩ B) = 0.2
APPEARS IN
संबंधित प्रश्न
A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine P(A or B).
The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?
In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that
- The student opted for NCC or NSS.
- The student has opted neither NCC nor NSS.
- The student has opted NSS but not NCC.
A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine
- P(2)
- P(1 or 3)
- P(not 3)
In a certain lottery, 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy one ticket.
A dice is thrown. Find the probability of getting:
2 or 4
In a simultaneous throw of a pair of dice, find the probability of getting a doublet of prime numbers
In a simultaneous throw of a pair of dice, find the probability of getting a sum greater than 9
In a simultaneous throw of a pair of dice, find the probability of getting an even number on first
In a simultaneous throw of a pair of dice, find the probability of getting neither 9 nor 11 as the sum of the numbers on the faces
In a simultaneous throw of a pair of dice, find the probability of getting a sum more than 7
In a simultaneous throw of a pair of dice, find the probability of getting neither a doublet nor a total of 10
In a simultaneous throw of a pair of dice, find the probability of getting a number greater than 4 on each die
In a simultaneous throw of a pair of dice, find the probability of getting a total of 9 or 11
In a simultaneous throw of a pair of dice, find the probability of getting a total greater than 8.
Three coins are tossed together. Find the probability of getting exactly two heads
Three coins are tossed together. Find the probability of getting at least one head and one tail.
A box contains 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that all are blue?
A box contains 6 red marbles numbered 1 through 6 and 4 white marbles numbered from 12 through 15. Find the probability that a marble drawn is even numbered
Fill in the blank in the table:
| P (A) | P (B) | P (A ∩ B) | P(A∪ B) |
| 0.35 | .... | 0.25 | 0.6 |
Fill in the blank in the table:
| P (A) | P (B) | P (A ∩ B) | P(A∪ B) |
| 0.5 | 0.35 | ..... | 0.7 |
There are three events A, B, C one of which must and only one can happen, the odds are 8 to 3 against A, 5 to 2 against B, find the odds against C
A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of its being a spade or a king.
In a single throw of two dice, find the probability that neither a doublet nor a total of 9 will appear.
A card is drawn from a deck of 52 cards. Find the probability of getting an ace or a spade card.
100 students appeared for two examination, 60 passed the first, 50 passed the second and 30 passed both. Find the probability that a student selected at random has passed at least one examination.
In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?
Find the probability of getting 2 or 3 tails when a coin is tossed four times.
One of the two events must occur. If the chance of one is 2/3 of the other, then odds in favour of the other are
If the probability of A to fail in an examination is \[\frac{1}{5}\] and that of B is \[\frac{3}{10}\] . Then, the probability that either A or B fails is
Three integers are chosen at random from the first 20 integers. The probability that their product is even is
A bag contains 5 black balls, 4 white balls and 3 red balls. If a ball is selected randomwise, the probability that it is black or red ball is
An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is
