Advertisements
Advertisements
प्रश्न
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?
उत्तर
The number of two digits can be formed from the given 9 digits in 9 × 9 = 81 different ways.
∴ n(S) = 81
Let A be the event that the number is even and less than 60.
Since the number is even, the unit place of two digits can be filled in 4P1 = 4 different ways by anyone of the digits 2, 4, 6, 8.
Also, the number is less than 60, so tenth place can be filled in 5P1 = 5 different ways by anyone of the digits 1, 2, 3, 4, 5.
∴ n(A) = 4 × 5 = 20
∴ Required probability = P(A) = `("n"("A"))/("n"("S")) = 20/81`
APPEARS IN
संबंधित प्रश्न
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 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 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?
A box contains 25 tickets numbered 1 to 25. Two tickets are drawn at random. What is the probability that the product on the numbers is even?
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')
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?
In a sample of 40 vehicles, 18 are red, 6 are trucks, of which 2 are red. Suppose that a randomly selected vehicle is red. What is the probability it is a truck?
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 ______
Let A and B be two events such that P(A) ≠ 1 and P(B) ≠ 0, then `"P"(bar"B"/bar"A")` = ______.
Let A and B be two events such that P(A) = 0.6, P(B) = 0.2, and P(A|B) = 0.5. Then P(A′|B′) equals ______.
Two cards are drawn from a well-shuffled deck of 52 playing cards with replacement. The probability, that both cards are queens, is ______.
A signal which can be green or red with probability 4/5 and 1/5 respectively, is received by station A and then trasmitted to station B. The probability of each station receiving the signal correctly is 3/4. If the signal received at station B is given, then the probability that the original signal is green, is
A bag contains 19 tickets, numbered from 1 to 19. Two tickets are drawn randomly in succession with replacement. Find the probability that both the tickets drawn are even numbers.
