Question 1

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.

Accepted Answer

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

Question 2

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?

Accepted Answer

Probability of getting 6 at the top once =1/6 Probability of getting 6 at the top three times =1/6 x 1/6 x 1/6 =216 Probability of no getting 6 at he top any time = 1 - 1/216 = 215/216

Question 3

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:

Accepted Answer

Let S be the sample space and E be the event of selecting 1 girl and 2 boys. Then, n(S) = Number ways of selecting 3 students out of 25 = 25 C 3 = 2300. n(E)= 10 C 1 * 15 C 2 = 1050. P(E) = n(E)/n(s) = 1050/2300 = 21/46

Question 4

What is the probabiltiy of getting a mutliple of 2 or 5 when an unbiased cubic die is thrown?

Accepted Answer

Total numbers in die=6 P(multiple of 2)=1/2 P(multiple of 5)=1/6 P(multiple of 2 or 5)=2/3

Question 5

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?

Accepted Answer

P(heart cards)=13/52 P(diamond cards)=13/52 P(heart or diamond)=13/52+13/52=1/2

Question 6

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?

Accepted Answer

P(red cards)=26/52 P(black cards)=26/52 P(red or black cards)=26/52+26/52=1

Question 7

Find the probability that it is either white or red ball when,one ball is drawn at random in a bag that contains 3 black,4 white and 5 red balls

Accepted Answer

P(red ball) = 5/12 P(white ball) = 4/12 P(red or white ball) = 5/12 + 4/12 = 3/4 = 0.75

Question 8

The odds favouring the event of a person hitting a target are 3 to 5. The odds against the event of another person hitting the target are 3 to 2. If each of them fire once at the target, find the probability that both of them hit the target.

Accepted Answer

Let A be the event of first person hitting the target, P ( A ) = 3 3 + 5 = 3 8 ( o d d i n f a v o u r ) Let B be the event of Second person hitting a target. P ( B ) = 2 3 + 2 = 2 5 ( o d d a g a i n s t ) Since both events are independent and both will hit the target so, P ( A ∩ B ) = P ( A ) P ( B ) = 3 8 × 2 5 = 3 20

Question 9

Find the probability of selecting 2 woman when four persons are choosen at random from a group of 3 men, 2 woman and 4 children.

Accepted Answer

Out of 9 persons,4 can be choosen in 9 C 4 ways =126. Favourable events for given condition = 2 C 2 * 7 C 2 = 21. So,required probability = 21/126 =1/6.

Question 10

In a lottery, there are 10 prizes and 25 blanks. A lottery is drawn at random. What is the probability of getting a prize ?

Accepted Answer

P(getting prize) = 10/ (10 + 25) =2/7

Question 11

A bag contains 3 black, 4 white and 5 red balls. One ball is drawn at random. Find the probability that it is either black or red ball:

Accepted Answer

P(black ball)=3/12 P(red ball)=5/12 P(black or red)=3/12+5/12=2/3

Question 12

What is the probability that a leap year selected at random, will contain 53 sundays?

Accepted Answer

In a leap year,there are 366 days=52 weeks and 2 days Remaining favourable 2 days can be sunday and monday or saturday and sunday Exhaustive number of cases =7 Favourable number of cases =2 So,required probability=2/7

Probability Questions