Advertisements
Advertisements
प्रश्न
A die is tossed thrice. Find the probability of getting an odd number at least once.
उत्तर
The total number obtained in the first throw of the dice = 6
And the case of not getting an odd number = 3
∴ Probability of not getting an odd number in the first toss P(A) = `3/6 = 1/2`
Similarly, the probability of not getting an odd number in the second toss is P(B) = `1/2`
Probability of not getting an odd number in the third toss P(C) = `1/2`
∵ The above three events are independent.
∴ The probability of all three happening together i.e. the event of not getting an odd number in each toss
P(A ∩ B ∩ C) = P(A) . P(B) . P(C)
= `1/2 . 1/2 . 1/2`
= `1/8`
∴ Probability of getting an odd number at least once
= 1 − P(A ∩ B ∩ C)
= `1 - 1/8`
= `7/8`
APPEARS IN
संबंधित प्रश्न
A fair coin is tossed five times. Find the probability that it shows exactly three times head.
Assume that each born child is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls? Given that
- the youngest is a girl.
- at least one is a girl.
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.
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find
- P(A ∩ B)
- P(A|B)
- P(A ∪ B)
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find P(A|B)
If P(A) = 0.8, P(B) = 0.5 and P(B|A) = 0.4, find P(A ∪ B)
If `P(A) = 6/11, P(B) = 5/11 "and" P(A ∪ B) = 7/11` find
- P(A ∩ B)
- P(A|B)
- P(B|A)
Determine P(E|F).
A coin is tossed three times, where
E: head on third toss, F: heads on first two tosses
Determine P(E|F).
A coin is tossed three times, where
E: at least two heads, F: at most two heads
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) and P (F|E)
Given that the two numbers appearing on throwing the two dice are different. Find the probability of the event ‘the sum of numbers on the dice is 4’.
If P(A) = `1/2`, P(B) = 0, then P(A|B) is ______.
Suppose we have four boxes. A, B, C and D containing coloured marbles as given below:
| Box | Marble colour | ||
| Red | White | Black | |
| A | 1 | 6 | 3 |
| B | 6 | 2 | 2 |
| C | 8 | 1 | 1 |
| D | 0 | 6 | 4 |
One of the boxes has been selected at random and a single marble is drawn from it. If the marble is red, what is the probability that it was drawn from box A?, box B?, box C?
A die is thrown again and again until three sixes are obtained. Find the probability of obtaining the third six in the sixth throw of the die.
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)
Two balls are drawn from an urn containing 3 white, 5 red and 2 black balls, one by one without replacement. What is the probability that at least one ball is red?
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.
A pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?
In an examination, 30% of students have failed in subject I, 20% of the students have failed in subject II and 10% have failed in both subject I and subject II. A student is selected at random, what is the probability that the student has failed in exactly one subject?
Three fair coins are tossed. What is the probability of getting three heads given that at least two coins show heads?
If A and B are two independent events such that P(A ∪ B) = 0.6, P(A) = 0.2, find P(B)
If for two events A and B, P(A) = `3/4`, P(B) = `2/5` and A ∪ B = S (sample space), find the conditional probability P(A/B)
Two thirds of students in a class are boys and rest girls. It is known that the probability of a girl getting a first grade is 0.85 and that of boys is 0.70. Find the probability that a student chosen at random will get first grade marks.
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
Find the probability that in 10 throws of a fair die a score which is a multiple of 3 will be obtained in at least 8 of the throws.
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 P(A ∩ B) = `7/10` and P(B) = `17/20`, then P(A|B) equals ______.
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:
A bag contains 3 red and 4 white balls and another bag contains 2 red and 3 white balls. If one ball is drawn from the first bag and 2 balls are drawn from the second bag, then find the probability that all three balls are of the same colour.
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 ______.
Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is draw from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ball is red, is ______.
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 ______.
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.
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 at least two of them will solve the problem.
Three friends go to a restaurant to have pizza. They decide who will pay for the pizza by tossing a coin. It is decided that each one of them will toss a coin and if one person gets a different result (heads or tails) than the other two, that person would pay. If all three get the same result (all heads or all tails), they will toss again until they get a different result.
- What is the probability that all three friends will get the same result (all heads or all tails) in one round of tossing?
- What is the probability that they will get a different result in one round of tossing?
- What is the probability that they will need exactly four rounds of tossing to determine who would pay?
