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