Navigate

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.

  • 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

  • 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

  • 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}

  • 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%

  • 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}

  • 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}