Advertisements
Advertisements
Question
Four cards are drawn from a pack of 52 cards. Find the probability that all cards are club and one of them a jack.
Solution
4 cards can be drawn out of 52 cards in 52C4 ways.
∴ n(S) = 52C4
Let D be the event that all the 4 cards drawn are clubs and one of them is a jack.
In a pack of 52 cards, there are 13 club cards having 1 jack card.
∴ 1 jack can be drawn in 1C1 way and the other 3 cards can be drawn from the remaining 12 club cards in 12C3 ways.
∴ n(D) = 1C1 × 12C3
∴ P(D) = `("n"("D"))/("n"("S"))`
= `(""^12"C"_3xx""^1"C"_1)/(""^52"C"_4)`
APPEARS IN
RELATED QUESTIONS
A fair die is thrown two times. Find the chance that Sum of the numbers on the upper face is at least 10.
A fair die is thrown two times. Find the chance that the first throw gives an odd number and second throw gives multiple of 3.
Two cards are drawn from a pack of 52 cards. Find the probability that both are black.
Two cards are drawn from a pack of 52 cards. Find the probability that both are ace cards.
Two cards are drawn from a pack of 52 cards. Find the probability that one is spade and other is non-spade.
Four cards are drawn from a pack of 52 cards. Find the probability that all the cards are from different suit.
Four cards are drawn from a pack of 52 cards. Find the probability that at least one heart.
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. What is the probability that, number on ticket is divisible by 6?
A box contains 75 tickets numbered 1 to 75. A ticket is drawn at random from the box. What is the probability that, number on ticket is prime?
From a group of 8 boys and 5 girls, a committee of five is to be formed. Find the probability that the committee contains 3 boys and 2 girls.
From a group of 8 boys and 5 girls, a committee of five is to be formed. Find the probability that the committee contains at least 3 boys.
A room has three sockets for lamps. From a collection of 10 light bulbs of which 6 are defective, a person selects 3 bulbs at random and puts them in socket. What is the probability that the room is lit?
The letters of the word LOGARITHM are arranged at random. Find the probability that vowels are always together.
The letters of the word LOGARITHM are arranged at random. Find the probability that vowels are never together.
The letters of the word LOGARITHM are arranged at random. Find the probability that Exactly 4 letters between G and H.
The letters of the word LOGARITHM are arranged at random. Find the probability that Begins with O and ends with T.
The letters of the word SAVITA are arranged at random. Find the probability that vowels are always together.
