Advertisements
Advertisements
Question
The probability of selecting a red ball at random from a jar that contains only red, blue and orange balls is 1/4. The probability of selecting a blue ball at random from the same jar 1/3. If the jar contains 10 orange balls, find the total number of balls in the jar.
Solution
Here the jar contains red, blue and orange balls.
Let the number of red balls be x.
Let the number of blue balls be y.
Number of orange balls = 10
Total number of balls = x + y + 10
Now, let P be the probability of drawing a ball from the jar
P(a red ball) =x/(x+x+10)
1/4=x/(x+x+10)
4x=x+x+10
3x-y=10.........(i)
Next
P(a blueball) =y/(x+x+10)
1/3=y/(x+x+10)
3y=x+x+10
2y-x=10 ......(ii)
Multiplying eq. (i) by 2 and adding to eq. (ii), we get
6x - 2y = 20
-x + 2y = 10
5x = 30
x=6
Subs. x = 6 in eq. (i), we get y = 8
Total number of balls = x + y + 10 = 6 + 8 + 10 = 24
Hence, total number of balls in the jar is 24.
RELATED QUESTIONS
A bag contains, white, black and red balls only. A ball is drawn at random from the bag.If the probability of getting a white ball is 3/10 and that of a black ball is 2/5 then find the
probability of getting a red ball. If the bag contains 20 black balls, then find the total number of balls in the bag.
A box contains 20 cards numbered from 1 to 20. A card is drawn at random from the box. Find the probability that the number on the drawn card is divisible by 2 or 3.
Two different dice are thrown together. Find the probability that the numbers obtained have
1) even sum, and
2) even product.
A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is a black king.
All the red face cards are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the drawn card is a queen.
Choose the correct alternative answer for the following question.
If n(A) = 2, P(A) = `1/5`, then n(S) = ?
A bag contains 3 red balls and 5 black balls. A ball is draw at random from the bag. What is the probability that the ball drawn is red?
A bag contains cards numbered from 1 to 49. A card is drawn from the bag at random, after mixing the card thoroughly. Find the probability that the number on the drawn card is an odd number
Red queens and black jacks are removed from a pack of 52 playing cards. A card is drawn at random from the remaining cards, after reshuffling them. Find the probability that the card drawn is a king
All red face cards are removed from a pack of playing cards. The remaining cards are well shuffled and then a card is drawn at random from them. Find the probability that the drawn card is a face card and
Suppose you drop a tie at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?
Cards each marked with one of the numbers 4, 5, 6, ..., 20 are placed in a box and mixed thoroughly. One card is drawn at random from the box. What is the probability of getting an even number?
Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn bears a number which is a multiple of 3?
A die is thrown once. Find the probability of getting a number less than 3.
A number is selected from numbers 1 to 25. The probability that it is prime is
A die is thrown once. Find the probability of getting a number which
lies between 2 and 6.
A coin is tossed twice. Find the probability of getting: two heads
In a single throw of a die, find the probability that the number:
(i) will be an even number.
(ii) will be an odd number.
(iii) will not be an even number.
In the experiment of tossing a coin one time, the outcome is either ______ or ______.
