Probability Problems Solutions

• 1. 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 :

  Option C

  Explanation:

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

• 2. 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 :

  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}

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

  1. 1
  2. 2/3
  3. 1/3
  4. 4/3

  Answer :

  Option B

  Explanation:

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

• 4. Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?

  1. 1/3
  2. 1/6
  3. 1/2
  4. 1/8

  Answer :

  Option C

  Explanation:

  Total cases are = 2*2*2 = 8, which are as follows
  [TTT, HHH, TTH, THT, HTT, THH, HTH, HHT]
  
  Favoured cases are = [TTH, THT, HTT, TTT] = 4
  
  So required probability = 4/8 = 1/2

• 5. In a throw of coin what is the probability of getting tails.

  1. 1
  2. 2
  3. 1/2
  4. 0

  Answer :

  Option C

  Explanation:

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

• 6. Two unbiased coins are tossed. What is probability of getting at most one tail ?

  1. \begin{aligned} \frac{1}{2} \end{aligned}
  2. \begin{aligned} \frac{1}{3} \end{aligned}
  3. \begin{aligned} \frac{3}{2} \end{aligned}
  4. \begin{aligned} \frac{3}{4} \end{aligned}

  Answer :

  Option D

  Explanation:

  Total 4 cases = [HH, TT, TH, HT]
  Favourable cases = [HH, TH, HT]
  Please note we need atmost one tail, not atleast one tail.
  
  So probability = 3/4

• 7. In a throw of coin what is the probability of getting head.

  1. 1
  2. 2
  3. 1/2
  4. 0

  Answer :

  Option C

  Explanation:

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