Advertisements
Advertisements
प्रश्न
Fill in the blank in the table:
| P (A) | P (B) | P (A ∩ B) | P(A∪ B) |
| \[\frac{1}{3}\] | \[\frac{1}{5}\] | \[\frac{1}{15}\] | ...... |
Advertisements
उत्तर
Given: \[P\left( A \right) = \frac{1}{3}, P\left( B \right) = \frac{1}{5} \text{ and } P\left( A \cap B \right) = \frac{1}{15}\]
By addition theorem, we have:
P (A ∪ B) = P(A) + P (B) - P (A ∩ B)
\[= \frac{1}{3} + \frac{1}{5} - \frac{1}{15}\]
\[= \frac{5 + 3 - 1}{15} = \frac{7}{15}\]
APPEARS IN
संबंधित प्रश्न
If `2/11` is the probability of an event, what is the probability of the event ‘not A’.
A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is
- a vowel
- an consonant
A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine P(not A).
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).
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.
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.
In a simultaneous throw of a pair of dice, find the probability of getting a doublet
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 less 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 total of 9 or 11
In a single throw of three dice, find the probability of getting a total of 17 or 18.
Two dice are thrown. Find the odds in favour of getting the sum 4.
Two dice are thrown. Find the odds in favour of getting the sum What are the odds against getting the sum 6?
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 white and odd numbered .
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 red or even numbered.
Fill in the blank in the table:
| P (A) | P (B) | P (A ∩ B) | P(A∪ B) |
| 0.5 | 0.35 | ..... | 0.7 |
If A and B are two events associated with a random experiment such that
P(A) = 0.5, P(B) = 0.3 and P (A ∩ B) = 0.2, find P (A ∪ B).
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.
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.
A person write 4 letters and addresses 4 envelopes. If the letters are placed in the envelopes at random, then the probability that all letters are not placed in the right envelopes, is
A and B are two events such that P (A) = 0.25 and P (B) = 0.50. The probability of both happening together is 0.14. The probability of both A and B not happening is
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
Out of 30 consecutive integers, 2 are chosen at random. The probability that their sum is odd, 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
A box contains 6 nails and 10 nuts. Half of the nails and half of the nuts are rusted. If one item is chosen at random, the probability that it is rusted or is a nail is
One mapping is selected at random from all mappings of the set A = {1, 2, 3, ..., n} into itself. The probability that the mapping selected is one to one is
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 10 tickets.
