Quantitative Aptitude: Probability Questions – Set 11

  1. In how many ways can 3 roses and 4 tulips 2 jasmines can be arranged in a garland such that all roses tied together and all tulips are tied together and jasmines also tied together?
    876
    864
    867
    912
    834
    Option B
    Required number of ways = 3( 3! * 4! *2!)
    =3* 3 * 2 * 4* 3 * 2 *2
    =>864 ways.

     

  2. In how many ways the word “ note book “ can be arranged?
    5670
    2456
    6720
    5670
    6120
    Option C
    notebook.
    There are 8 letters. o is repeated three times
    So number of words formed=8!/ 3!
    =6720 ways

     

  3. There are two positive integers x and y .What is the probability that x+y is even?
    1/2
    1/3
    1/4
    1/5
    1/6
    Option A
    Sum of positive integers is either odd or even.
    Hence the required probability= ½

     

  4. The sum of three consecutive odd number is 93.Then what will be the middle number if they arranged in descending order?
    30
    31
    29
    33
    35
    Option B
    Let the three numbers be 2a +1 , 2a+3, 2a +5
    Given 2a+1 + 2a+3 +2a+ 5= 93
    =>6a +6 = 93
    => 6a= 84
    =>a=14
    Hence the numbers are = 29,31,33
    So the middle number is 31.

     

  5. A bag contains 6 nestle bars and 4 kitkat bars. Two bars given at random to the children.
    Then what is the probability that they are of same bars?
    2/15
    3/15
    5/15
    6/25
    7/15
    Option E
    Required probability = 6C2 + 4C2 / 10C2
    = 30+ 12/ 90 = 42/90
    =7/15

     

  6. In how many different words can be formed from word ENCYCLOPEDIA such that all vowels come together?
    20150
    20140
    20160
    20980
    20790
    Option C
    NCYCLPD(all vowels)
    So number of letters= 8 also c is repeated twice.
    Required probability = 8!/ 2! = 20160 ways

     

  7. Out of all the 2-digit integers between 1 and 50, a 2-digit number has to be selected at random.
    What is the probability that the selected number is not divisible by 13?
    31/40
    32/40
    25/40
    33/40
    37/40
    Option E
    There are total 40 two digit numbers, out of them 3 are divisible by 13, these are 13, 26, 39
    Therefore, probability that selected number is not divisible by 13 = 1 – 3/40 = 37/40

     

  8. How many different words can be arranged with letters of the word STENCIL when vowels occupied even places?
    620
    720
    360
    440
    580
    Option B
    Vowels are 2, places are 3. So they are arranged in 6 ( 3C2 * 2! ) ways.
    Consonants can be arranged in 5! = 120 ways.
    Total arrangement = 720 ways( 120*6).

     

  9. There are 2 red balls, 5 orange and 4 purple balls .Two balls are drawn at random.What is the probability that one is red the other is orange or purple?
    12/55
    11/55
    16/55
    18/55
    17/55
    Option D
    There are 2 red balls and 9 other color balls. So total balls= 11
    2 balls drawn at random,
    => required probablity= 2C1 * 9C1/11C2
    =2*9/11*10/2
    =>36/110 =18/55

     

  10. There are 8 students are selected from dance school for dance competition.The total number of students are 18.
    In how many ways can be the selection be made so that 2 students are always included?
    8008
    5005
    6006
    7007
    9009
    Option A
    If 2 members are always included
    The total number of ways= 2C2 * 16 C 2
    =8008

     

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