# Probability Questions Answers

1) Bag contain 10 back and 20 white balls, One ball is drawn at random. What is the probability that ball is wh

- 1) 1
- 2) 2/3
- 3) 1/3
- 4) 4/3

**Ans.**B

**Explanation :**

Total cases = 10 + 20 = 30 Favourable cases = 20 So probability = 20/30 = 2/3

2) In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked up randomly. What is the probability that it is neither blue nor gree

- 1) 2/3
- 2) 8/21
- 3) 3/7
- 4) 9/22

**Ans.**B

**Explanation :**

Total number of balls = (8 + 7 + 6) = 21 Let E = event that the ball drawn is neither blue nor green =e vent that the ball drawn is red. Therefore, n(E) = 8. P(E) = 8/21.

3) A card is drawn from a pack of 52 cards. The probability of getting a queen of club or a king of heart

- 1) 1/13
- 2) 2/13
- 3) 1/26
- 4) 1/52

**Ans.**C

**Explanation :**

Total number of cases = 52 Favourable cases = 2 Probability = 2/56 = 1/26

4) From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card dra

- 1) 4/13
- 2) 1/52
- 3) 1/4
- 4) None of above

**Ans.**A

**Explanation :**

Total number of cases = 52 Total face cards = 16 [favourable cases] So probability = 16/52 = 4/13

5) A box contains 20 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective

- 1) \begin{aligned} \frac{7}{19} \end{aligned}
- 2) \begin{aligned} \frac{6}{19} \end{aligned}
- 3) \begin{aligned} \frac{5}{19} \end{aligned}
- 4) \begin{aligned} \frac{4}{19} \end{aligned}

**Ans.**A

**Explanation :**

Please remember that Maximum portability is 1. So we can get total probability of non defective bulbs and subtract it form 1 to get total probability of defective bulbs. So here we go, Total cases of non defective bulbs \begin{aligned} ^{16}C_2 = \frac{16*15}{2*1} = 120 \\text{total cases = } \ ^{20}C_2 = \frac{20*19}{2*1} = 190 \\text{probability = } \frac{120}{190} = \frac{12}{19} \\text{P of at least one defective = } 1- \frac{12}{19} \=\frac{7}{19} \end{aligned}

6) A speaks truth in 75% of cases and B in 80% of cases. In what percentage of cases are they likely to contradict each other, narrating the same incid

- 1) 30%
- 2) 35%
- 3) 40%
- 4) 45%

**Ans.**B

**Explanation :**

Let A = Event that A speaks the truth B = Event that B speaks the truth Then P(A) = 75/100 = 3/4 P(B) = 80/100 = 4/5 P(A-lie) = 1-3/4 = 1/4 P(B-lie) = 1-4/5 = 1/5 Now A and B contradict each other = [A lies and B true] or [B true and B lies] = P(A).P(B-lie) + P(A-lie).P(B) [Please note that we are adding at the place of OR] = (3/5*1/5) + (1/4*4/5) = 7/20 = (7/20 * 100) % = 35%

7) From a pack of 52 cards, two cards are drawn together, what is the probability that both the cards are ki

- 1) 2/121
- 2) 2/221
- 3) 1/221
- 4) 1/13

**Ans.**C

**Explanation :**

\begin{aligned} \text{Total cases =} ^{52}C_2 \ = \frac{52*51}{2*1} = 1326 \\text{Total King cases =} ^{4}C_2 \\ = \frac{4*3}{2*1} = 6 \ \text{Probability =} = \frac{6}{1326}\ = \frac{1}{221} \\ \end{aligned}

8) A box contains 5 green, 4 yellow and 3 white balls. Three balls are drawn at random. What is the probability that they are not of same colo

- 1) 52/55
- 2) 3/55
- 3) 41/44
- 4) 3/44

**Ans.**C

**Explanation :**

\begin{aligned} \text{Total cases =} ^{12}C_3 \\ = \frac{12*11*10}{3*2*1} = 220 \\ \text{Total cases of drawing same colour =} \ ^{5}C_3 + ^{4}C_3 + ^{3}C_3 \\ \frac{5*4}{2*1} + 4 + 1 = 15 \ \text{Probability of same colur =} = \frac{15}{220}\\ = \frac{3}{44} \\ \text{Probability of not same colur =} \ 1-\frac{3}{44}\\ = \frac{41}{44} \end{aligned}

9) In a throw of coin what is the probability of getting hea

- 1) 1
- 2) 2
- 3) 1/2
- 4) 0

**Ans.**C

**Explanation :**

Total cases = [H,T] - 2 Favourable cases = [H] -1 So probability of getting head = 1/2

10) In a throw of coin what is the probability of getting tail

- 1) 1
- 2) 2
- 3) 1/2
- 4) 0

**Ans.**C

**Explanation :**

Total cases = [H,T] - 2 Favourable cases = [T] -1 So probability of getting tails = 1/2