Probability Problems Solutions

• 8. What is the probability of getting a sum 9 from two throws of dice.

  1. 1/3
  2. 1/9
  3. 1/12
  4. 2/9

  Answer :

  Option B

  Explanation:

  Total number of cases = 6*6 = 36
  
  Favoured cases = [(3,6), (4,5), (6,3), (5,4)] = 4
  
  So probability = 4/36 = 1/9

• 9. 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 :

  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%
  
  

• 10. 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 :

  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}

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

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

  Answer :

  Option A

  Explanation:

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

• 12. In a throw of dice what is the probability of getting number greater than 5

  1. 1/2
  2. 1/3
  3. 1/5
  4. 1/6

  Answer :

  Option D

  Explanation:

  Number greater than 5 is 6, so only 1 number
  Total cases of dice = [1,2,3,4,5,6]
  
  So probability = 1/6

• 13. 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 :

  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}

• 14. 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 :

  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.