Advertisements
Advertisements
प्रश्न
Four cards are successively drawn without replacement from a deck of 52 playing cards. What is the probability that all the four cards are kings?
उत्तर
Let E1, E2, E3 and E4 be the events that first, second, third and fourth card is King respectively.
∴ P(E1 ∩ E2 ∩ E3 ∩ E4)
= `"P"("E"_1) * "P"("E"_2/"E"_1) . "P"["E"_3/(("E"_1 ∩ "E"_2))] * "P"["E"_4/(("E"_1 ∩ "E"_2 ∩ "E"_3 ∩ "E"_4))]`
= `4/52 xx 3/51 xx 2/50 xx 1/49`
= `24/(52*51*50*49)`
= `1/(13*17*25*49)`
= `1/27075`
Hence, the required probability is `1/27075`.
APPEARS IN
संबंधित प्रश्न
There are 6% defective items in a large bulk of items. Find the probability that a sample of 8 items will include not more than one defective item.
A coin is tossed 5 times. What is the probability of getting at least 3 heads?
A coin is tossed 5 times. What is the probability that tail appears an odd number of times?
State the sample space and n(S) for the following random experiment.
A coin is tossed twice. If a second throw results in a tail, a die is thrown.
A coin and a die are tossed. State sample space of following event.
B: Getting a prime number.
Find total number of distinct possible outcomes n(S) of the following random experiment.
5 balls are randomly placed into 5 cells, such that each cell will be occupied.
Find total number of distinct possible outcomes n(S) of the following random experiment.
6 students are arranged in a row for a photograph.
Two dice are thrown. Write favourable Outcomes for the following event.
P: Sum of the numbers on two dice is divisible by 3 or 4.
A card is drawn at random from an ordinary pack of 52 playing cards. State the number of elements in the sample space if consideration of suits is not taken into account.
Consider an experiment of drawing two cards at random from a bag containing 4 cards marked 5, 6, 7, and 8. Find the sample Space if cards are drawn with replacement.
Consider an experiment of drawing two cards at random from a bag containing 4 cards marked 5, 6, 7, and 8. Find the sample Space if cards are drawn without replacement.
From a group of 2 men (M1, M2) and three women (W1, W2, W3), two persons are selected. Describe the sample space of the experiment. If E is the event in which one man and one woman are selected, then which are the cases favourable to E?
There are 2 red and 3 black balls in a bag. 3 balls are taken out at random from the bag. Find the probability of getting 2 red and 1 black ball or 1 red and 2 black balls.
A box has 5 blue and 4 red balls. One ball is drawn at random and not replaced. Its colour is also not noted. Then another ball is drawn at random. What is the probability of second ball being blue?
A die is thrown 5 times. Find the probability that an odd number will come up exactly three times.
The probability of a man hitting a target is 0.25. He shoots 7 times. What is the probability of his hitting at least twice?
A die is thrown three times. Let X be ‘the number of twos seen’. Find the expectation of X.
Two natural numbers r, s are drawn one at a time, without replacement from the set S = {1, 2, 3, ...., n}. Find P[r ≤ p|s ≤ p], where p ∈ S.
An urn contains m white and n black balls. A ball is drawn at random and is put back into the urn along with k additional balls of the same colour as that of the ball drawn. A ball is again drawn at random. Show that the probability of drawing a white ball now does not depend on k.
A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement the probability of getting exactly one red ball is ______.
A flashlight has 8 batteries out of which 3 are dead. If two batteries are selected without replacement and tested, the probability that both are dead is ______.
Two dice are thrown. If it is known that the sum of numbers on the dice was less than 6, the probability of getting a sum 3, is ______.
A box has 100 pens of which 10 are defective. What is the probability that out of a sample of 5 pens drawn one by one with replacement at most one is defective?
Three horses A, B, Care in a race. A is twice as likely to win as B, and B is twice as likely to win as C. The probability that C wins, P(C) is
The probability of getting qualified in JEE-Mains and JEE-Advanced by a student are `1/5` and `3/5` respectively. The probability that the students gets qualified for one of these tests is
A box contains 10 balls, of which 3 are red, 2 are yellow, and 5 are blue. Five balls are randomly selected with replacement. Calculate the probability that fewer than 2 of the selected balls are red?
A bag contains 10 white and 3 black balls. Balls are drawn without replacement till all the black balls are drawn. What is the probability that this procedure will come to an end on the seventh draw?
An urn contains 5 red and 2 green balls. A ball is drawn at random from the urn. If the drawn ball is green, then a red ball is added to the urn and if the drawn ball is red, then a green ball is added to the urn; the original ball is not returned to the urn. Now, a second ball is drawn at random from it. The probability that the second ball is red is:
