Advertisements
Advertisements
प्रश्न
A problem in Mathematics is given to three students whose chances of solving it are `1/3, 1/4` and `1/5`. What is the probability that the problem is solved?
Advertisements
उत्तर
Let A1 denote the event of that first student solves the problem.
A2 denote the event that second student solves the problem.
A3 denote the event that third student solves the problem.
Given P(A1) = `1/3`
P(A2) = `1/4`
P(A3) = `1/5`
We note that A1, A2, A3 are independent events.
The problem will be solved if atleast one of them
solves it we have to find P(A1 ∪ A2 ∪ A3)
Probability of at least one solves the problem = 1 – Probability of no one solving it
P(A1 ∪ A2 ∪ A3) = `1 - "P"(bar"A"_1 ∪ bar"A"_2 ∪ bar"A"_3)`
= `1 - "P"(bar"A"_1) * "P"("A"_2) * "P"("A"_3)`
A1, A2, A3 are independent then `bar"A"1, bar"A"_2, bar"A"_3` are also independent.
= 1 – [1 – p(A1)] [1 – P(A2)] [1 – P(A3)]
= `1 - (1 - 1/3) (1 - 1/4) (1 - 1/5)`
= `1 - (2/3) (3/4) (4/5)`
= `1 - 2/5`
= `(5 - 2)/5`
= `3/5
APPEARS IN
संबंधित 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.
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 pair of dice is thrown. If sum of the numbers is an even number, what is the probability that it is a perfect square?
A bag contains 10 white balls and 15 black balls. Two balls are drawn in succession without replacement. What is the probability that, one is white and other is black?
Three fair coins are tossed. What is the probability of getting three heads given that at least two coins show heads?
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
If P(A) = 0.5, P(B) = 0.8 and P(B/A) = 0.8, find P(A/B) and P(A ∪ B)
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 both are black
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.
Given P(A) = 0.4 and P(A ∪ B) = 0.7 Find P(B) if P(B/A) = 0.5
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
If P(A) = `4/5`, and P(A ∩ B) = `7/10`, then P(B|A) 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:
A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is ______.
Let A and B be two non-null events such that A ⊂ B. Then, which of the following statements is always correct?
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 ______.
Compute P(A|B), if P(B) = 0.5 and P (A ∩ B) = 0.32.
Which complement form is correct when \[P(B)\neq 0\]?
Which sequence correctly applies a given condition when finding a conditional probability?
