Advertisements
Advertisements
प्रश्न
A card from a pack of 52 playing cards is lost. From the remaining cards of the pack three cards are drawn at random (without replacement) and are found to be all spades. Find the probability of the lost card being a spade.
उत्तर
Let E1, E2, E3, E4 and A be the event defined as below:
E1 = the missing card is a heart card
E2 = the missing card is a spade card
E3 = the missing card is a club card
E4 = the missing card is a diamond card
A = drawing three spade cards from the remaining cards
Now, we have the following:
`P(E_1)=13/52=1/4`
`P(E_2)=13/52=1/4`
`P(E_3)=13/52=1/4`
`P(E_4)=13/52=1/4`
`P(A/E_1)=(""^13C_3)/(""^51C_3)`
`P(A/E_2)=(""^12C_3)/(""^51C_3)`
`P(A/E_3)=(""^13C_3)/(""^51C_3)`
`P(A/E_4)=(""^13C_3)/(""^51C_3)`
By Bayes Theorem, we have:
Required probability =`P(E_2/A)`
`=(P(E_1)P(A/E_2))/(P(A/E_1)E_1+P(A/E_2)E_2+P(A/E_3)E_3+P(A/E_4)E_4)`
`=(1/4xx(""^13C_3)/(""^51C_3))/((""^13C_3)/(""^51C_3)xx1/4+(""^12C_3)/(""^51C_3)xx1/4+(""^13C_3)/(""^51C_3)xx1/4+(""^13C_3)/(""^51C_3)xx1/4)`
`=(""^12C_3)/(""^12C_3+3xx""^13C_3)`
`=220/(220+286xx3)=110/539`
APPEARS IN
संबंधित प्रश्न
A speaks truth in 60% of the cases, while B in 90% of the cases. In what percent of cases are they likely to contradict each other in stating the same fact? In the cases of contradiction do you think, the statement of B will carry more weight as he speaks truth in more number of cases than A?
A die, whose faces are marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.
A fair coin and an unbiased die are tossed. Let A be the event ‘head appears on the coin’ and B be the event ‘3 on the die’. Check whether A and B are independent events or not.
Let E and F be events with `P(E) = 3/5, P(F) = 3/10 and P(E ∩ F) = 1/5`. Are E and F independent?
Given two independent events A and B such that P (A) = 0.3, P (B) = 0.6. Find
- P (A and B)
- P(A and not B)
- P(A or B)
- P(neither A nor B)
A fair die is rolled. If face 1 turns up, a ball is drawn from Bag A. If face 2 or 3 turns up, a ball is drawn from Bag B. If face 4 or 5 or 6 turns up, a ball is drawn from Bag C. Bag A contains 3 red and 2 white balls, Bag B contains 3 red and 4 white balls and Bag C contains 4 red and 5 white balls. The die is rolled, a Bag is picked up and a ball is drawn. If the drawn ball is red; what is the probability that it is drawn from Bag B?
A problem in statistics is given to three students A, B, and C. Their chances of solving the problem are `1/3`, `1/4`, and `1/5` respectively. If all of them try independently, what is the probability that, problem is not solved
The odds against a certain event are 5: 2 and odds in favour of another independent event are 6: 5. Find the chance that at least one of the events will happen.
Select the correct option from the given alternatives :
The odds against an event are 5:3 and the odds in favour of another independent event are 7:5. The probability that at least one of the two events will occur is
Solve the following:
Consider independent trails consisting of rolling a pair of fair dice, over and over What is the probability that a sum of 5 appears before sum of 7?
10% of the bulbs produced in a factory are of red colour and 2% are red and defective. If one bulb is picked up at random, determine the probability of its being defective if it is red.
If A and B′ are independent events then P(A′ ∪ B) = 1 – ______.
Refer to Question 1 above. If the die were fair, determine whether or not the events A and B are independent.
A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A ∩ B) = `1/4`. Find: `"P"("A'"/"B'")`
Two dice are tossed. Find whether the following two events A and B are independent: A = {(x, y): x + y = 11} B = {(x, y): x ≠ 5} where (x, y) denotes a typical sample point.
If A and B are two events such that P(A) = `1/2`, P(B) = `1/3` and P(A/B) = `1/4`, P(A' ∩ B') equals ______.
If A and B are two events and A ≠ Φ, B ≠ Φ, then ______.
In Question 64 above, P(B|A′) is equal to ______.
If A and B are mutually exclusive events, then they will be independent also.
Two independent events are always mutually exclusive.
If A and B are independent, then P(exactly one of A, B occurs) = P(A)P(B') + P(B)P(A')
If A and B are two events such that P(A) > 0 and P(A) + P(B) >1, then P(B|A) ≥ `1 - ("P"("B'"))/("P"("A"))`
Let E1 and E2 be two independent events. Let P(E) denotes the probability of the occurrence of the event E. Further, let E'1 and E'2 denote the complements of E1 and E2, respectively. If P(E'1 ∩ E2) = `2/15` and P(E1 ∩ E'2) = `1/6`, then P(E1) is
The probability that A hits the target is `1/3` and the probability that B hits it, is `2/5`. If both try to hit the target independently, find the probability that the target is hit.
The probability of the event A occurring is `1/3` and of the event B occurring is `1/2`. If A and B are independent events, then find the probability of neither A nor B occurring.
