Advertisements
Advertisements
Question
Two cards are drawn one after the other from a pack of 52 cards with replacement. What is the probability that both the cards drawn are face cards?
Advertisements
Solution
Two cards are drawn from a pack of 52 cards with replacement.
n(S) = 52 × 52
Let A be the event that two cards drawn are face cards.
First card from 12 face cards is drawn with replacement in 12C1 = 12 ways
and second face card is drawn from 12 face card in 12C1 = 12 ways after replacement.
∴ n(A) = 12 × 12
∴ P (that both the cards drawn are face cards)
= P(A) = `("n"("A"))/("n"("S")`
= `(12xx12)/(52xx52)`
= `9/169`
APPEARS IN
RELATED QUESTIONS
A bag contains 5 white and 4 black balls and another bag contains 7 white and 9 black balls. A ball is drawn from the first bag and two balls are drawn from the second bag. What is the probability of drawing one white and two black balls?
A box contains 11 tickets numbered from 1 to 11. Two tickets are drawn at random with replacement. If the sum is even, find the probability that both the numbers are odd.
A card is drawn from a well-shuffled pack of 52 cards. Consider two events A and B as
A: a club 6 card is drawn.
B: an ace card 18 drawn.
Determine whether the events A and B are independent or not.
A bag contains 4 blue and 5 green balls. Another bag contains 3 blue and 7 green balls. If one ball is drawn from each bag, what is the probability that two balls are of the same colour?
Two throws are made, the first with 3 dice and the second with 2 dice. The faces of each die are marked with the number 1 to 6. What is the probability that the total in first throw is not less than 15 and at the same time the total in the second throw is not less than 8?
A number of two digits is formed using the digits 1, 2, 3, ….., 9. What is the probability that the number so chosen is even and less than 60?
For two events A and B of a sample space S, if P(A) = `3/8` , P(B) = `1/2` and P(A ∪ B) = `5/8` . Find the value of the following: P(A' ∩ B')
For two events A and B of a sample space S, if P(A) =` 3/8`, P(B) = `1/2` and P(A ∪ B) = `5/8`. Find the value of the following: P(A' ∪ B')
For two events A and B of a sample space S, if P(A ∪ B) = `5/6`, P(A ∩ B) = `1/3` and P(B') = `1/3`, then find P(A).
A bag contains 3 red marbles and 4 blue marbles. Two marbles are drawn at random without replacement. If the first marble drawn is red, what is the probability the second marble is blue?
A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability that both are yellow?
A speaks truth in 80% of the cases and B speaks truth in 60% of the cases. Find the probability that they contradict each other in narrating an incident
A company produces 10,000 items per day. On a particular day, 2500 items were produced on machine A, 3500 on machine B, and 4000 on machine C. The probability that an item is produced by the machines. A, B, C to be defective is respectively 2%, 3%, and 5%. If one item is selected at random from the output and is found to be defective, then the probability that it was produced by machine C, is ______
Two cards are drawn from a well-shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is ______.
Teena is practising for an upcoming Rifle Shooting tournament. The probability of her shooting the target in the 1st, 2nd, 3rd and 4th shots are 0.4, 0.3, 0.2 and 0.1 respectively. Find the probability of at least one shot of Teena hitting the target.
