Advertisements
Advertisements
प्रश्न
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
Advertisements
उत्तर
Total number of balls = 10 + 15 = 25
Let S be event that two balls are drawn at random without replacement in succession
∴ n(S) = `""^25"C"_1xx""^24"C"_1` = 25 × 24
Let A be the event that the first ball is white and second is black.
First white ball can be drawn from 10 white balls in 10C1 ways and second black ball can be drawn from 15 black balls in 15C1 ways.
∴ n(A) = `""^10"C"_1xx""^15"C"_1`
∴ P(A) = `("n"("A"))/("n"("S"))=(""^10"C"_1xx""^15"C"_1) /(25xx24)=(10xx15)/(25xx24)=1/4`
APPEARS IN
संबंधित प्रश्न
A fair coin is tossed five times. Find the probability that it shows exactly three times head.
40% students of a college reside in hostel and the remaining reside outside. At the end of the year, 50% of the hostelers got A grade while from outside students, only 30% got A grade in the examination. At the end of the year, a student of the college was chosen at random and was found to have gotten A grade. What is the probability that the selected student was a hosteler ?
Determine P(E|F).
A coin is tossed three times, where
E: at least two heads, F: at most two heads
An instructor has a question bank consisting of 300 easy True/False questions, 200 difficult True/False questions, 500 easy multiple choice questions and 400 difficult multiple choice questions. If a question is selected at random from the question bank, what is the probability that it will be an easy question given that it is a multiple-choice question?
Two balls are drawn at random with replacement from a box containing 10 black and 8 red balls. Find the probability that
- both balls are red.
- first ball is black and second is red.
- one of them is black and other is red.
A card is drawn from a well-shuffled pack of playing cards. What is the probability that it is either a spade or an ace or both?
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in subject I, if it is known that he is failed in subject II?
An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement, What is the probability that at least one ball is black?
Two balls are drawn from an urn containing 5 green, 3 blue, and 7 yellow balls one by one without replacement. What is the probability that at least one ball is blue?
Three fair coins are tossed. What is the probability of getting three heads given that at least two coins show heads?
Select the correct option from the given alternatives :
Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. The probability that it was drawn from Bag II
Can two events be mutually exclusive and independent simultaneously?
If A and B are two events such that P(A ∪ B) = 0.7, P(A ∩ B) = 0.2, and P(B) = 0.5, then show that A and B are independent
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(A/B) = 0.4
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball is ______
Find the probability that in 10 throws of a fair die a score which is a multiple of 3 will be obtained in at least 8 of the throws.
If P(A) = `2/5`, P(B) = `3/10` and P(A ∩ B) = `1/5`, then P(A|B).P(B'|A') is equal to ______.
For a biased dice, the probability for the different faces to turn up are
| Face | 1 | 2 | 3 | 4 | 5 | 6 |
| P | 0.10 | 0.32 | 0.21 | 0.15 | 0.05 | 0.17 |
The dice is tossed and it is told that either the face 1 or face 2 has shown up, then the probability that it is face 1, is ______.
