Advertisements
Advertisements
Question
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?
Advertisements
Solution
Two tickets can be drawn out of 25 tickets in 25C2 = `(25 xx 24)/(1 xx 2)` = 300 ways.
∴ n(S) = 300
Let A be the event that product of two numbers is even.
This is possible if both numbers are even, or one number is even, and other is odd.
As there are 13 odd numbers and 12 even numbers from 1 to 25.
∴ n(A) = `""^12"C"_1 + ""^12"C"_1 xx ""^13"C"_1`
= `(12 xx 11)/(1 xx 2) + 12 xx 13`
= 66 + 156
= 222
∴ Required probability = P(A)
= `("n"("A"))/("n"("S")`
= `222/300`
= `37/50`
APPEARS IN
RELATED QUESTIONS
Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.
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.
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 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 box contains 10 red balls and 15 green balls. Two balls are drawn in succession without replacement. What is the probability that, the first is red and the second is green?
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 ______.
An electric instrument consists of two units. Each unit must function independently for the instrument to operate. The probability that the first unit functions is 0.9 and that of the second unit is 0.8. The instrument is switched on and it fails to operate. If the probability that only the first unit failed and second unit is functioning is p, then 98 p is equal to
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.
