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Probability Test 8
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Probability Test 8
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  • Question 1/10
    1 / -0

    From a pack of 52 cads, 2 cards are drawn at random. What is the probability of drawing such that there is at least 1 king?

    Solutions

    Explanation: 

    Case 1: 1 is king

    4C1*48C1 / 52C2

    Case 2: both are king

    4C2 / 52C2

    Add both cases.

     

  • Question 2/10
    1 / -0

    A box contains 6 blue, 5 green and 4 red balls. If two balls are pick at random, then what is the probability that neither is blue? 

    Solutions

    Explanation: 

    Total balls = 15

    Not blue means green or red i.e. any of (5+4) = 9 balls

    So prob. = 9C2 / 15C2

     

  • Question 3/10
    1 / -0

    A box contains 5 blue and 5 white balls. What is the probability of drawing 2 balls such that both are same in color? 

    Solutions

    Explanation: 

    Case 1: Both blue

    5C2 / 10C2

    Case 2: Both white

    5C2 / 10C2

     

    Add both cases.

  • Question 4/10
    1 / -0

    A committee of 4 people is to be formed from 3 men, 2 women and 4 children. What is the probability that exactly two of chosen people are children? 

    Solutions

    Explanation: 

    2 children should be there and rest 2 either from (2 women + 3 men) 5 people

    So prob. = 4C2*5C2/ 9C4

     

  • Question 5/10
    1 / -0

    In a class 30% of the students opt for Math, 20% opt for Computers and 10% opt for both. A student is selected at random, find the probability that he has opted either Math or Computers. 

    Solutions

    Explanation: 

    Prob. of math = 30/100 = 3/10, Prob. of computers = 20/100 = 1/5, prob. for both = 10/100 = 1/10

    So required prob. = 3/5 + 1/5 – 1/10

     

  • Question 6/10
    1 / -0

    From a pack of 52 cards, 2 cards are drawn at random. What is the probability that either both are red or both are kings? 

    Solutions

    Explanation: 

    Prob. of both red = 26C2/52C2

    Prob. of both kings = 4C2/52C2

    Since there are also cads which are both red and king, so we will subtract there prob. There are 2 red cards which are kings

    Prob. of both red and king = 2C2/52C2

    So required prob. = 26C2/52C2 + 4C2/52C2 – 2C2/52C2

     

  • Question 7/10
    1 / -0

    A box contains 10 electric bulbs from which 2 bulbs are defective. Two bulbs are chosen at random. What is the probability that one of them is defective? 

    Solutions

    Explanation: 

    2C1*8C1/10C2

     

  • Question 8/10
    1 / -0

    A bag contains 8 blue and 7 green balls. A ball is drawn out of it and put back in the bag. Then a ball is drawn again. What is the probability that both the balls are green? 

    Solutions

    Explanation: 

    7/15 * 7/15

     

  • Question 9/10
    1 / -0

    A bag contains 8 blue and 7 green balls. 2 balls are drawn one by one without replacement. What is the probability that the balls are alternately of different colors? 

    Solutions

    Explanation: 

    When 1st is blue, prob. = 8/15 * 7/14

    When 1st is green, prob. = 7/15 * 8/14

    Add both cases.

     

  • Question 10/10
    1 / -0

    There are 5 men and 3 women. A committee of 3 members is to be made. Find the probability that either there are 2 men and 1 woman or 2 women and 1 man. 

    Solutions

    Explanation: 

    2 men and 1 woman, prob. = 5C2*3C1/8C3

    2 women and 1 man, prob. = 5C1*3C2/8C3

    Add both cases

     

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