Advertisements
Advertisements
Question
Two cards are drawn from a pack of 52 cards. Find the probability that both are red cards
Solution
Two cards can be drawn from a pack of 52 cards in 52C2 = `(52 xx 51)/(1 xx 2)` = 26 × 51 ways
∴ n(S) = 26 × 51
Let D ≡ the event that both the cards are red cards
There are 26 red cards
∴ two red cards can be chosen in 26C2
= `(26xx25)/(1xx2)`
= 13 × 25 ways
∴ n(D) = 13 × 25
∴ the reqwred probability = P(D) = `("n"("D"))/("n"("S"))`
= `(13 xx 25)/(26 xx 51)`
= `25/102`
APPEARS IN
RELATED QUESTIONS
A fair die is thrown two times. Find the probability that sum of the numbers on them is 5
A fair die is thrown two times. Find the probability that sum of the numbers on them is at least 8
A fair die is thrown two times. Find the probability that the first throw gives a multiple of 2 and the second throw gives a multiple of 3.
A fair die is thrown two times. Find the probability that the product of numbers on them is 12.
Two cards are drawn from a pack of 52 cards. Find the probability that one is club and the other is a diamond.
Two cards are drawn from a pack of 52 cards. Find the probability that both are from the same suit.
Two cards are drawn from a pack of 52 cards. Find the probability that one is a heart card and the other is a non-heart card
Three cards are drawn from a pack of 52 cards. Find the chance that two are queen cards and one is an ace card
Three cards are drawn from a pack of 52 cards. Find the chance that all are from the same suit
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement vowels are always together.
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement vowels are never together
Letters of the word MOTHER are arranged at random. Find the probability that in the arrangement O is at the begining and end with T
15 professors have been invited for a round table conference by Vice chancellor of a university. What is the probability that two particular professors occupy the seats on either side of the Vice chancellor during the conference
A bag contains 7 black and 4 red balls. If 3 balls are drawn at random find the probability that one is black and two are red.
Form a group of 4 men, 4 women and 3 children, 4 persons are selected at random. Find the probability that, no child is selected.
Select the correct option from the given alternatives :
There are 2 shelves. One shelf has 5 Physics and 3 Biology books and the other has 4 Physics and 2 Biology books. The probability of drawing a Physics book is
Select the correct option from the given alternatives :
Two friends A and B apply for a job in the same company. The chances of A getting selected is `2/5` and that of B is `4/7`. The probability that both of them get selected is
Solve the following:
An urn contains 5 red balls and 2 green balls. A ball is drawn. If its green, a red ball is added to the urn and if its red, a green ball is added to the urn. (The original ball is not returned to the urn). Then a second ball is drawn. What is the probability that the second ball is red?
Solve the following:
Suppose that five good fuses and two defective ones have been mixed up. To find the defective fuses, we test them one-byone, at random and without replacement. What is the probability that we are lucky and fine both of the defective fuses in the first two tests?
Solve the following:
A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that both the children are girls
Solve the following:
A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that both the children are girls given that at least one of them is a girl
Ram is visiting a friend. Ram knows that his friend has 2 children and 1 of them is a boy. Assuming that a child is equally likely to be a boy or a girl, then the probability that the other child is a girl, is ______.
Four persons work independently on a task. If the respective probabilities that they will solve it are 1/5, 1/3, 1/7, and 1/6, then the probability that none can solve it is ______
A coin is tossed 9 times. The probability of obtaining at most one head is ______
If three dices are thrown then the probability that the sum of the numbers on their uppermost faces to be atleast 5 is ______.
There are two bags. One bag contains 4 blue pens and 3 black pens. The other bag contains 7 red pens and 3 black pens. If a bag is selected at random and from it, a pen is drawn, the probability that the pen is black is ______
An unbiased die with faces marked 1, 2, 3, 4, 5 and 6 is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than 2 and the maximum face value is not greater than 5, is ______.
If two letters of the word MOTHER are selected at random. Probability that both are consonants is ______.
In a simultaneous toss of five coins, the probability of getting exactly four tails is ______.
A die is thrown four times. The probability of getting perfect square in at least one throw is ______.
Probability that a person will develop immunity after vaccinations is 0.8. if 8 people are given the vaccine, then probability that all develop immunity is = ______.
Probability of guessing correctly atleast 7 out of 10 answers in a ‘True’ or ‘False’ test is equal to ______.
If 15 coupons are numbered 1, 2, 3, ..., 15, respectively. 7 coupons are selected at random one at a time with replacement. The probability that the largest number appearing on a selected coupon is almost 9, is ______.
