Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Let A and B represent the events of opted NCC and NSS respectively.
Total number of students = 60
Number of students who opted for NCC = 30
Probability of being selected for NCC P(A) = `30/60 = 1/2`
Number of students who opted for N.S.S. = 32
∴ Probability of being selected for N.S.S. P(B) = `32/60`
Number of people who opted for NCC and NSS = 24
Probability of opted for NCC and NSS = `24/60`
(i) Probability of being selected for NCC and NSS P(A ∪ B) = P(A) + P(B) – P(A ∩ B)
= `30/60 + 32/60 - 24/60`
= `38/60`
= `19/30`
(ii) The probability of not selecting either NCC or NSS
P(A’ ∩ B’) = P[(A ∪ B)’]
= 1 – P(A ∪ B)
= `1 - 19/30`
= `11/30`
(iii) The student has opted for NSS but not NCC
Its probability = P(A’ ∩ B) = P(B) – P(A ∩ B)
= `32/60 - 24/60`
= `8/60`
= `2/15`
APPEARS IN
संबंधित प्रश्न
If `2/11` is the probability of an event, what is the probability of the event ‘not A’.
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).
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).
In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.
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?
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:
2 or 4
In a simultaneous throw of a pair of dice, find the probability of getting a doublet of odd 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 6
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 single throw of three dice, find the probability of getting a total of 17 or 18.
Three coins are tossed together. Find the probability of getting exactly two heads
Two dice are thrown. Find the odds in favour of getting the sum 5.
Two dice are thrown. Find the odds in favour of getting the sum What are the odds against getting the sum 6?
What are the odds in favour of getting a spade if the card drawn from a well-shuffled deck of cards? What are the odds in favour of getting a king?
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 .
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 .
Fill in the blank in the table:
| P (A) | P (B) | P (A ∩ B) | P(A∪ B) |
| 0.35 | .... | 0.25 | 0.6 |
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.
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?
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
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
A box contains 10 good articles and 6 defective articles. One item is drawn at random. The probability that it is either good or has a defect, is
A box contains 10 good articles and 6 with defects. One item is drawn at random. The probability that it is either good or has a defect 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 two tickets.
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.
