Advertisements
Advertisements
Question
If E and F are events such that P(E) = `1/4`, P(F) = `1/2` and P(E and F) = `1/8`, find
- P(E or F)
- P(not E and not F).
Advertisements
Solution
P(E) = `1/4`, P(F) = `1/2`, P(E and F) = P(E ∩ B) = `1/8`
(i) P (E) or F) = P(E U F) = P(E) + P(F) – P(E ∩ F)
= `1/4 + 1/2 - 1/8`
= `(2 + 4 - 1)/8`
= `5/8`
(ii) P(not E and not F) = P(E ∩ F)
= P[(E ∪ F)'] = 1 – P(E ∪ F)
= `1 - 5/8`
= `3/8`
APPEARS IN
RELATED QUESTIONS
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
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?
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)
Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
A dice is thrown. Find the probability of getting a prime number
A dice is thrown. Find the probability of getting a multiple of 2 or 3.
In a simultaneous throw of a pair of dice, find the probability of getting:
8 as the sum
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 an even number on first
In a simultaneous throw of a pair of dice, find the probability of getting odd number on the first and 6 on the second
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 single throw of three dice, find the probability of getting a total of 17 or 18.
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 .
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 |
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).
One of the two events must happen. Given that the chance of one is two-third of the other, find the odds in favour of the other.
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.
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 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.
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
Two dice are thrown simultaneously. The probability of getting a pair of aces 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
Five persons entered the lift cabin on the ground floor of an 8 floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first, then the probability of all 5 persons leaving at different floor is
