Find the probability that one ball is white when two balls are drawn at random f

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Question
Find the probability that one ball is white when two balls are drawn at random from a basket that contains 9 red, 7 white and 4 black balls.
Options
A. 18/95
B. 18/190
C. 1/2
D. 91/190

Correct Answer

91/190

Explanation

Total number of elementary events = $20 C_{2}$ ways =190

There are 7 white balls out of which one white can be drawn in 7 $C_{1}$ ways and one ball from remaining 13 balls can be drawn in $13 C_{1}$ ways.

So,favourable events = $7 C_{1} * 13 C_{1}$

Therfore,required probability = ( $7 C_{1} * 13 C_{1}$ )/ $20 C_{2}$ =91/90

Probability problems

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1. One card is drawn from deck of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the ball drawn is red.
Options
A. 1/3
B. 1/2
C. 1/4
D. 1/6

2. Find the probability of selecting exactly 2 children when four persons are choosen at random from a group of 3 men, 2 woman and 4 children.
Options
A. 9/29
B. 10/21
C. 12/21
D. 14/19

3. What is the probability that a couple with four children have atleast one girl?
Options
A. 0.0625
B. 0.9375
C. 0.5
D. 0.0257

4. The probability that a card drawn at random from the pack of playing cards may be either a queen or an ace is:
Options
A. 9/13
B. 11/13
C. 2/13
D. None of these

5. The probabiltiy that throw of two dice yields a total of 5 or 6 is:
Options
A. 2/14
B. 5/18
C. 3/4
D. 1/4

6. A six-sided die with faces numbered 1 through 6 is rolled three times. What is the probability that the face with the number 6 on it will not face upward on all the three rolls?
Options
A. 215/216
B. 1/216
C. 215/256
D. 1/52

7. In a class, there are 15 boys and 10 girls. Three students are selected at random. The probability that 1 girl and 2 boys are selected, is:
Options
A. 21/46
B. 1/5
C. 3/25
D. 1/50

8. What is the probabiltiy of getting a mutliple of 2 or 5 when an unbiased cubic die is thrown?
Options
A. 1/3
B. 1/2
C. 2/3
D. 1/6

9. What is the probability that it is either a heart card or diamond card, when a card is drawn from a well shuffled standard pack of 52 playing cards?
Options
A. 1
B. 1/2
C. 3/4
D. 1/3

10. From well shuffled standard pack of 52 playing cards,one card is drawn. What is the probability that it is either a red card or black card?
Options
A. 1/2
B. 3/4
C. 1
D. 1/3

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