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Probability Test 5
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Probability Test 5
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  • Question 1/10
    1 / -0

    16 persons are participated in a party. In how many different ways can they host the seat in a circular table, if the 2 particular persons are to be seated on either side of the host ?

    Solutions

    Explanation :(16 – 2)! * 2 = 14! * 2

     

  • Question 2/10
    1 / -0

    Out of a total 10 bulbs, 6 bulbs are working inorder. One has to choose 2 bulbs out of 6. What is the probability that all the 2 bulbs will be glowing ?

    Solutions

    Explanation :

    6C2 = 6*5/2*1 = 30/2 = 15

    10C2  = 10*9/1*2 = 45

    P =15/45 = 1/3

     

  • Question 3/10
    1 / -0

    In how many different ways can the letters of the word KINETIC arranged so that the vowels never come together ?      

    Solutions

    Explanation :

    7 letters = 7! /2!= 5040/2 = 2520

    Vowels => I I E = 3!/2! =6/2 = 3

    Consonants 4 + all vowels considered as 1 = 4+1 = 5 => 5! = 120

    120*3 = 360

    No of ways the vowels never come together = 2520 – 360 = 2160

     

  • Question 4/10
    1 / -0

    A bag contains 4 black shirts , 3 yellow shirts and 5 red shirts, if 2 shirts are drawn randomly, What is the probability both of them are black?

    Solutions

    Explanation :

    12C2 = 12*11/2 = 66

    4C2 = 4*3/2 = 12/2 = 6

    P = 6/66 = 1/11

     

  • Question 5/10
    1 / -0

    A box contains 10 white balls and 6 black balls. 2 balls are drawn at random. What is the probability that they are of the same colour ?

    Solutions

    Explanation :

    10C2 = 10*9/2 = 45

    6C2 = 6*5/2 = 15

    16C2 = 16*15/2 = 120

    P = 45+15/120 = 60/120 = 1/2

     

  • Question 6/10
    1 / -0

    An urn contains 4 brown marbles, 5 green marbles, 2 red marbles and 3 white marbles. If 3 marbles are drawn, what is the probability all of them is green ?

    Solutions

    Explanation :

    Total = 14

    3 marbles drawn = 14C3 = 14*13*12/ 3*2*1 = 364

    5C3 = 5*4*3/3*2*1 = 10

    P = 10/364 = 5/182

     

  • Question 7/10
    1 / -0

    A basket contains 3 brown and 4 green balls. If three balls are drawn at random ,What is the probability that all the three are same colour?

    Solutions

    Explanation :

    Total = 3+4 = 7

    7C3 = 7*6*5/3*2*1 = 35

    3C3 + 4C3 = 1 + 4*3*2 /3*2*1 = 1+4 = 5

    P  = 5/35 = 1/7

     

  • Question 8/10
    1 / -0

    In how many different ways the word FAVOUR can be arranged ?

    Solutions

    Explanation :6! = 6*5*4*3*2*1 = 720

     

  • Question 9/10
    1 / -0

    A bag contains 5 white and 3 red balls. One ball is drawn at random. What is the probability that the ball drawn is red?

    Solutions

    Explanation :

    Total = 5+3 = 8

    Red = 3

    P = 3/8

     

  • Question 10/10
    1 / -0

    From a group of  4 men ,3 women, 2 persons are selected at random, Find the probability at least one man is selected ?

    Solutions

    Explanation :

    7C2 = 7*6/2 = 21

    4C1*3C1 + 4C2 = 4*3 + (4*3)/2 = 12+6 = 18

    P = 18/21 = 6/7

     

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