Advertisements
Advertisements
प्रश्न
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?
Advertisements
उत्तर
When 3 dice are thrown, then the sample space S1 has 6 × 6 × 6 = 216 sample points.
∴ n(S1) = 216
Let A be the event that the sum of the numbers is not less than 15.
∴ A = {(3,6,6), (4,5,6), (4,6,5), (4,6,6), (5,4,6), (5,5,5), (5,5,6), (5,6,4), (5,6,5), (5,6,6), (6,3,6), (6,4,5), (6,4,6), (6,5,4), (6,5,5), (6,5,6), (6,6,3), (6,6,4), (6,6,5), (6,6,6)}
∴ n(A) = 20
∴ P(A) = `("n"("A"))/("n"("S"_1)) = 20/216 = 5/54`
When 2 dice are thrown, the sample space S2 has 6 × 6 = 36 sample points.
∴ n(S2) = 36
Let B be the event that sum of numbers is not less than 8.
∴ B = {(2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}
∴ n(B) = 15
∴ P(B) = `("n"("B"))/("n"("S"_2)) = 15/36 = 5/12`
A ∩ B = Event that the total in the first throw is not less than 15 and at the same time the total in the second throw is not less than 8
∵ A and B are independent events
∴ P(A ∩ B) = P(A).P(B) = `5/54 xx 5/12 = 25/648`
APPEARS IN
संबंधित प्रश्न
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 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 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?
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 ∪ B) = `5/6`, P(A ∩ B) = `1/3` and P(B') = `1/3`, then find P(A).
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 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")` = ______.
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
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.
A box contains 9 tickets numbered 1 to 9, both inclusive. If 3 tickets are drawn from the box one at a time, then the probability that they are alternatively either {odd, even, odd} or {even, odd, even} is
Which formula gives the Multiplication Theorem for two events when \[P(F) \ne 0\]?
Which expression gives the probability of three events occurring together?
An urn contains 10 black balls and 5 white balls. If \[E\] is the event “first ball is black,” what is \[P(E)\]?
Two balls are drawn one after another without replacement from an urn containing 10 black balls and 5 white balls. What is the probability that both balls are black?
For the event “both balls are black,” which expression correctly applies the Multiplication Theorem?
What should always be done before solving a probability problem using the Multiplication Theorem?
