Advertisements
Advertisements
Question
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.
Advertisements
Solution
Two tickets are drawn from 11 tickets numbered 1 to 11 with replacement
∴ n(S) = 11C1 x 11C1 = 121
Let A be the event that the sum of two numbers is even.
The event A occurs, if either both the tickets with odd numbers or both the tickets with even numbers are drawn.
There are 6 odd numbers (1, 3, 5, 7, 9, 11) and 5 even numbers (2, 4, 6, 8, 10) from 1 to 11.
∴ n(A) = 6 × 6 + 5 × 5 = 36 + 25 = 61
∴ P(A) = `("n"("A"))/("n"("S")) = 61/121`
Let B be the event that the numbers tickets drawn are odd
∴ n(B) = 6 × 6 = 36
∴ P(B) = `("n"("B"))/("n"("S")) = 36/121`
Since 6 odd numbers are common between A and B
∴ n(A ∩ B) = 6 × 6 = 36
∴ P(A ∩ B) = `("n"("A" ∩ "B"))/("n"("S")) = 36/121`
∴ Probability of both the numbers are odd, given that sum is even, is given by
`"P"("B"/"A") = ("P"("A" ∩ "B"))/("P"("A")`
= `(36/121)/(61/121)`
= `36/61`
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 of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale
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 25 tickets numbered 1 to 25. Two tickets are drawn at random. What is the probability that the product on the numbers is even?
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?
A bag contains 8 red balls and 5 white balls. Two successive draws of 3 balls are made without replacement. Find the probability that the first drawing will give 3 white balls and second drawing will give 3 red balls.
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')
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 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
Let A and B be two events such that P(A) ≠ 1 and P(B) ≠ 0, then `"P"(bar"B"/bar"A")` = ______.
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
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
