Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
Let A and B be the events of passing English and Hindi examinations, respectively.
Accordingly, we have:
P(A and B) = 0.5
P(not A and not B) = 0.1 [i.e. P(A' ∩ B') = 0.1]
P(A) = 0.75
Now, P(A∪B) + P(A' ∩ B') = 1
⇒ P(A∪B) = 1 - P(A' ∩ B')
= 1 -0.1 = 0.9
By addition theorem, we have:
P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
⇒ 0.9 = 0.75 + P (B) - 0.5
⇒ P(B) = 0.9 - 0.75 + 0.5
⇒ P(B) = 0.65
Thus, the probability of passing the Hindi examination is 0.65.
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
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?
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.
Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that
- you both enter the same sections?
- you both enter the different sections?
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 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 6
In a simultaneous throw of a pair of dice, find the probability of getting a total greater than 8.
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 10 red marbles, 20 blue marbles and 30 green marbles. 5 marbles are drawn at random. From the box, what is the probability that at least one is green?
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) |
| \[\frac{1}{3}\] | \[\frac{1}{5}\] | \[\frac{1}{15}\] | ...... |
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 ∪ B) = 0.8, P (A ∩ B) = 0.3 and P \[(\bar{A} )\]= 0.5, find P(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.
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
The probability that a leap year will have 53 Fridays or 53 Saturdays is
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
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
