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 ?
Evaluate P(A ∪ B), if 2P(A) = P(B) = `5/13` and P(A | B) = `2/5`
Determine P(E|F).
Two coins are tossed once, where
E: tail appears on one coin, F: one coin shows head
Determine P(E|F).
A die is thrown three times,
E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses
A black and a red dice are rolled.
Find the conditional probability of obtaining a sum greater than 9, given that the black die resulted in a 5.
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P (E|G) and P (G|E)
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P ((E ∪ F)|G) and P ((E ∩ G)|G)
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.
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?
Box I contains two white and three black balls. Box II contains four white and one black balls and box III contains three white ·and four black balls. A dice having three red, two yellow and one green face, is thrown to select the box. If red face turns up, we pick up the box I, if a yellow face turns up we pick up box II, otherwise, we pick up box III. Then, we draw a ball from the selected box. If the ball is drawn is white, what is the probability that the dice had turned up with a red face?
Two dice are thrown simultaneously, If at least one of the dice show a number 5, what is the probability that sum of the numbers on two dice is 9?
A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?
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?
If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)
One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that both are black
A year is selected at random. What is the probability that it contains 53 Sundays
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.
A Problem in Mathematics is given to the three students A, B and C. Their chances of solving the problem are `1/2, 1/3` and `1/4` respectively. Find the probability that at least two of them will solve the problem.
