Probability Questions Answers

• 8. 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 green?

  1. 2/3
  2. 8/21
  3. 3/7
  4. 9/22

  Answer And Explanation

  Answer: Option 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.

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

  1. 1/13
  2. 2/13
  3. 1/26
  4. 1/52

  Answer And Explanation

  Answer: Option C

  Explanation:

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

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• 10. From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn.

  1. 3/13
  2. 1/52
  3. 1/4
  4. None of above

  Answer And Explanation

  Answer: Option A

  Explanation:

  Total number of cases = 52
  
  Total face cards = 12 [favourable cases]
  
  
  
  So probability = 12 /52 = 3/13

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• 11. 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 is

  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. $$\begin{aligned} \frac{4}{19} \end{aligned}$$

  Answer And Explanation

  Answer: Option 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
  $$\begin{aligned} ^{16}C_2 = \frac{16*15}{2*1} = 120 \\ \text{total cases = } \\ ^{20}C_2 = \frac{20*19}{2*1} = 190 \\ \text{probability = } \frac{120}{190} = \frac{12}{19} \\ \text{P of at least one defective = } 1- \frac{12}{19} \\ =\frac{7}{19} \end{aligned}$$

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• 12. 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 incident

  1. 30%
  2. 35%
  3. 40%
  4. 45%

  Answer And Explanation

  Answer: Option 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%
  
  

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• 13. From a pack of 52 cards, two cards are drawn together, what is the probability that both the cards are kings

  1. 2/121
  2. 2/221
  3. 1/221
  4. 1/13

  Answer And Explanation

  Answer: Option C

  Explanation:

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

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• 14. 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 colour.

  1. 52/55
  2. 3/55
  3. 41/44
  4. 3/44

  Answer And Explanation

  Answer: Option C

  Explanation:

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

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