Advertisements
Advertisements
Question
If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is ______.
Options
`1/9`
`4/9`
`1/18`
`1/2`
Advertisements
Solution
If the sum of numbers obtained on throwing a pair of dice is 9, then the probability that number obtained on one of the dice is 4, is `underlinebb(1/2)`.
Explanation:
When two dice are thrown, then
Total probable cases, n(S) = 36
Cases when the sum of 9 is obtained,
A = (3, 6), (6, 3), (4, 5), (5, 4)
n(A) = 4
∴ P(A) = `4/36 = 1/9`
Now, cases when there is 4 on one of dice (sum is 9).
B = (4, 5), (5, 4),
∴ n(A ∩ B) = 2
P(A ∩ B) = `2/36`
Required probability
`P(B/A) = (P(B ∩ A))/(P(A))`
= `(2/36)/(4/36)`
= `1/2`
APPEARS IN
RELATED QUESTIONS
An insurance agent insures lives of 5 men, all of the same age and in good health. The probability that a man of this age will survive the next 30 years is known to be 2/3 . Find the probability that in the next 30 years at most 3 men will survive.
Given that E and F are events such that P(E) = 0.6, P(F) = 0.3 and P(E ∩ F) = 0.2, find P (E|F) and P(F|E).
Determine P(E|F).
A die is thrown three times,
E: 4 appears on the third toss, F: 6 and 5 appears respectively on first two tosses
A black and a red dice are rolled.
Find the conditional probability of obtaining the sum 8, given that the red die resulted in a number less than 4.
A fair die is rolled. Consider events E = {1, 3, 5}, F = {2, 3} and G = {2, 3, 4, 5} Find P ((E ∪ F)|G) and P ((E ∩ G)|G)
Consider the experiment of throwing a die, if a multiple of 3 comes up, throw the die again and if any other number comes, toss a coin. Find the conditional probability of the event ‘the coin shows a tail’, given that ‘at least one die shows a 3’.
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A ∩ B = Φ.
If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?
If A and B are events such as that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`, then find
1) P(A / B)
2) P(B / A)
A box has 20 pens of which 2 are defective. Calculate the probability that out of 5 pens drawn one by one with replacement, at most 2 are defective.
In a college, 70% of students pass in Physics, 75% pass in Mathematics and 10% of students fail in both. One student is chosen at random. What is the probability that:
(i) He passes in Physics and Mathematics?
(ii) He passes in Mathematics given that he passes in Physics.
(iii) He passes in Physics given that he passes in Mathematics.
An urn contains 4 black, 5 white, and 6 red balls. Two balls are drawn one after the other without replacement, What is the probability that at least one ball is black?
Select the correct option from the given alternatives :
Bag I contains 3 red and 4 black balls while another Bag II contains 5 red and 6 black balls. One ball is drawn at random from one of the bags and it is found to be red. The probability that it was drawn from Bag II
The probability that a car being filled with petrol will also need an oil change is 0.30; the probability that it needs a new oil filter is 0.40; and the probability that both the oil and filter need changing is 0.15. If a new oil filter is needed, what is the probability that the oil has to be changed?
One bag contains 5 white and 3 black balls. Another bag contains 4 white and 6 black balls. If one ball is drawn from each bag, find the probability that one white and one black
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if A and B are independent events
A year is selected at random. What is the probability that it is a leap year which contains 53 Sundays
Three machines E1, E2, E3 in a certain factory produced 50%, 25% and 25%, respectively, of the total daily output of electric tubes. It is known that 4% of the tubes produced one each of machines E1 and E2 are defective, and that 5% of those produced on E3 are defective. If one tube is picked up at random from a day’s production, calculate the probability that it is defective.
Let A and B be two events. If P(A) = 0.2, P(B) = 0.4, P(A ∪ B) = 0.6, then P(A|B) is equal to ______.
If two balls are drawn from a bag containing 3 white, 4 black and 5 red balls. Then, the probability that the drawn balls are of different colours is:
If A and B are two events such that P(A) = `1/3`, P(B) = `1/5` and P(A ∪ B) = `1/2`, then P(A|B') + P(B|A') is equal to ______.
If A and B are two independent events such that P(A) = `1/3` and P(B) = `1/4`, then `P(B^'/A)` is ______.
A Problem in Mathematics is given to the three students A, B and C. Their chances of solving the problem are `1/2, 1/3` and `1/4` respectively. Find the probability that exactly two students will solve the problem.
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
Which statement is the multiplication rule for two events A and B?
Which complement form is correct when \[P(B)\neq 0\]?
Which sequence correctly applies a given condition when finding a conditional probability?
