Advertisements
Advertisements
प्रश्न
A bag contains 5 white balls and some blue balls. If the probability of drawing a blue ball is double that of a white ball, determine the number of blue balls in the bag
उत्तर
Let the number of blue balls be x.
Number of white balls = 5
∴ Total number of balls = (x + 5)
P(blue ball is drawn) = `x/(x + 5)`
P(white ball is drawn) = `5/(x + 5)`
According to the given condition, the probability of drawing a blue ball is double that of a white ball.
∴ P(blue ball is drawn) = 2 × P(white ball is drawn)
∴ `x/(x +5) = 2 xx 5/(x + 5)`
∴ x(x + 5) = 10(x + 5)
∴ x2 + 5x = 10x + 50
∴ x2 – 5x – 50 = 0
∴ x2 – 10x + 5x – 50 = 0
∴ x(x – 10) + 5(x – 10) = 0
∴ (x – 10)(x + 5) = 0
∴ x – 10 = 0 or x + 5 = 0
∴ x = 10 or x = – 5
But, number of balls cannot be negative.
∴ x = 10
∴ The number of blue balls in the bag is 10.
APPEARS IN
संबंधित प्रश्न
Three coins are tossed simultaneously, find S and n(S).
Two-digit numbers are formed from the digits 0,1,2,3,4 where digits are not repeated. Find the probability of the events that:
(a) The number formed is an even number.
(b) The number formed is a prime number.
A card is drawn from a well shuffled pack of 52 playing cards. Find the probability of the event, the card drawn is a red card.
Activity: Let ‘S’ be the sample space.
∴ n(S) = 52
Event A: Card drawn is a red card.
∴ Total red cards = `square` hearts + 13 diamonds
∴ n(A) = `square`
∴ P(A) = `square/(n("S"))` ......[Formula]
P(A) = `26/52`
P(A) = `square`
If two dice are rolled simultaneously, find the probability of the following events.
Event B: The sum of the digits on the upper faces is 33
If three coins are tossed simultaneously, find the probability of the following events
Event A: To get no head.
A box contains 36 cards, bearing only one number from 1 to 36 on each. If one card is drawn at random, find the probability of an event that the card drawn bears, a number divisible by 3
A bag contains 8 red balls and some blue balls. If one ball is drawn randomly the probability of drawing a red ball to a blue ball are in the ratio 5 : 2, determine the probability of drawing a blue ball from the bag.
A bag contains 8 red and some blue balls. One ball is drawn at random from the bag. If ratio of probability of getting red ball and blue ball is 2:5, then find the number of blue balls.
Let A be an event. For event A, which probability cannot be possible?
Let E be an event and P(E) = `6/7`, then find the value of P(not E).
In a workshop, there are five machines and the probability of any one of them to be out of service on a day is `1/4`. If the probability that at most two machines will be out of service on the same day is `(3/4)^3k`, then k is equal to ______.
If six students, including two particular students A and B, stand in a row, then the probability that A and B are separated with one student in between them is ______.
For three events A, B and C, P(Exactly one of A or B occurs) = P(Exactly one of B or C occurs) = P(Exactly one of C or A occurs) = `1/4` and P(All three events occur simultaneously) = `1/16`. Then the probability that at least one of the events occurs is ______.
From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one woman. Then the probability for these committees to have more women than men is ______.
A two digit number is formed with digits 2, 3, 5, 7, 9 without repetition. What is the probability of the following events?
Event A : The number formed is an odd number.
Event B : The number formed is a multiple of 5.
A card is drawn from well shuffled pack of 52 playing cards. Find the probability that the card drawn is a face card.
One coin and a die are thrown simultaneously. Find the probability of the following event:
Event A: To get a head and a prime number.
One coin and a die are thrown simultaneously. Find the probability of the following event:
Event B: To get a tail and an odd number.
