Advertisements
Advertisements
प्रश्न
A die is thrown three times. Events A and B are defined as below:
A : 5 on the first and 6 on the second throw.
B: 3 or 4 on the third throw.
Find the probability of B, given that A has already occurred.
Advertisements
उत्तर
A is an event of getting 5 on the first throw and 6 on the second throw.
Then
A={(5,6,1) (5,6,2) (5,6,3) (5,6,4) (5,6,5) (5,6,6)}
Also, B is an event of getting 3 or 4 on the third throw.
∴ A∩B={(5,6,3), (5,6,4)}
Required probability, `P(A|B)=(n(A∩B))/(n(A))=2/6=1/3`
Thus, the probability of B, given that A has already occurred is 1/3
APPEARS IN
संबंधित प्रश्न
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.
The probability that a certain kind of component will survive a check test is 0.6. Find the probability that exactly 2 of the next 4 tested components 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).
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)
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.
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’.
If P(A) = `1/2`, P(B) = 0, then P(A|B) is ______.
A and B are two events such that P (A) ≠ 0. Find P (B|A), if A is a subset of B.
If a leap year is selected at random, what is the chance that it will contain 53 Tuesdays?
Five dice are thrown simultaneously. If the occurrence of an odd number in a single dice is considered a success, find the probability of maximum three successes.
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 subject I, if it is known that he is failed in subject II?
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, first is white and second is black?
From a pack of well-shuffled cards, two cards are drawn at random. Find the probability that both the cards are diamonds when the first card drawn is replaced in the pack
Suppose the chances of hitting a target by a person X is 3 times in 4 shots, by Y is 4 times in 5 shots, and by Z is 2 times in 3 shots. They fire simultaneously exactly one time. What is the probability that the target is damaged by exactly 2 hits?
Choose the correct alternative:
If A and B are any two events, then the probability that exactly one of them occur is
Choose the correct alternative:
A letter is taken at random from the letters of the word ‘ASSISTANT’ and another letter is taken at random from the letters of the word ‘STATISTICS’. The probability that the selected letters are the same is
The total number of ways in which 5 balls of different colours can be distributed among 3 persons so that each person gets at least one ball 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.
If P(A) = `3/10`, P(B) = `2/5` and P(A ∪ B) = `3/5`, then P(B|A) + P(A|B) equals ______.
Two cards are drawn out randomly from a pack of 52 cards one after the other, without replacement. The probability of first card being a king and second card not being a king is:
If P(A) = `1/2`, P(B) = 0, then `P(A/B)` is
If A and B are two events such that `P(A/B) = 2 xx P(B/A)` and P(A) + P(B) = `2/3`, then P(B) is equal to ______.
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.
Which complement form is correct when \[P(B)\neq 0\]?
For \[E=\{(b,b)\}\] and \[F=\{(b,b),(g,b),(b,g)\}\], what are \[E\cap F\], \[P(E\cap F)\], and \[P(F)\]?
Which statement correctly describes the numerator in \[P(A\mid B)=\frac{P(A\cap B)}{P(B)}\]?
For independent events, which equality holds provided \[P(B)\neq 0\]?
