QUESTION ON PROBABILITY

QUES 1:

There are 8 Male and 7 Female Persons in a Committee we have to select 4 persons for a group.

A)     What is the probability that 3 Male and 1 Female person is there ?

(i)                  25/39     (ii)           56/195  (iii)          11/39     (iv)         156/195                (v)          None of these

B)      What is the probability that atleast 1 Female person is there ?

(i)                  37/39     (ii)           85/195  (iii)          11/195  (iv)         65/195                  (v)          None of these

C)      What is the probability that atmost 2  Male persons is there ?

(i)                  5/63       (ii)           56/165  (iii)          11/65     (iv)         43/65                     (v)          None of these

D)     What is the probability that no Female person is there ?

(i)                  5/39       (ii)           6/195     (iii)          2/39       (iv)         56/195                  (v)          None of these

QUES 2:

In a college 6 Arts, 8 Commerce and 5 Science teachers are there.

A)     If 5 teachers are seleted at random, then what is the probability that 2 Arts, 2 Commerce and 1 science teacher is there?

(i)            175/969                (ii)           65/969  (iii)          64/323  (iv)         6/19       (v)          None of these

B)      If 4 teachers are seleted at random, then what is the probability that no Commerce  teacher is there?

(i)            5/323     (ii)           5/646     (iii)          1/11       (iv)         55/646  (v)          None of these

C)      If 3 teachers are seleted at random, then what is the probability that atleast 1 Arts  teacher is there?

(i)            5/9         (ii)           56/969  (iii)          37/39     (iv)         683/969                (v)          None of these

D)     If 3 teachers are seleted at random, then what is the probability that exactly 1 science teacher and 2 other than science teachers are there?

(i)                  55/969  (ii)           455/969                (iii)          1/69       (iv)         56/69     (v)          None of these

QUES 3:

A bag contains 5 Red, 3 Green, 2 Blue and 4 Yellow balls.

A)     If 2 balls are drawn randomly, what is the probability that both are Yellow ?

(i)            1/28       (ii)           6/91       (iii)          3/14       (iv)         1/9         (v)          None of these

B)      If 3 balls are drawn randomly, what is the probability that 2 are Green and 1 is Yellow ?

(i)            3/14       (ii)           2/91       (iii)          9/182     (iv)         3/91       (v)          None of these

C)      If 3 balls are drawn randomly, what is the probability that atleast 1 is Red ?

(i)                  10/13     (ii)           1/13       (iii)          3/13       (iv)         2/13       (v)          None of these

ANSWERS :

QUES 1 :                              

A)     (ii)

B)      (i)

C)      (iv)

D)     (iii)

QUES 2 :

A)     (i)

B)      (iv)

C)      (iv)

D)     (ii)

QUES 3 :

A)     (ii)

B)      (iv)

C)      (i)

QUESTIONS BASED ON PROBABILITY

QUES 1:

An urn contains 6 Red, 4 Blue, 2 Green and 3 Yellow marbles.

(a)    If two marbles are picked at random, what is the probability that both are Red?

(i)                  1/7         (ii)          1/3         (iii)          2/15       (iv)         2/5         (v) None of these

(b)   If three marbles are picked at random, what is the probability that two are Blue and one is Yellow ?

(i)                  3/91       (ii)           1/5         (iii)          18/455  (iv)         7/15       (v) None of these

(c)    If four marbles are picked at random, what is the probability that at least one is Blue?

(i)                  4/15       (ii)           69/91     (iii)          11/15     (iv)         22/91     (v) None of these

(d)   If two marbles are picked at random, what is the probability that either both are Green or both are Yellow ?

(i)                  5/91       (ii)           1/35       (iii)          1/3         (iv)         4/105     (v) None of these

(e)   If four marbles are picked at random, what is the probability that one is Green, two are  Blue and one is Red?

(i)                  24/455  (ii)           13/35     (iii)          11/15     (iv)         7/91       (v) None of these

QUES 2:

 A bag contains 3 Red balls, 5 Blue balls and 6 Green balls.

(a)    If three balls are randomly drawn from  the bag, then what is the probability that all are Blue coloured ?

(i)                  3/18       (ii)           5/182     (iii)          25/182 (iv)         1/4        (v)          None of these

(b)   If three balls are randomly drawn from the bag, then what is the probability that 2 are Green and 1 is Red.

(i)                  54/364  (ii)           2 5/182 (iii)          15/364  (iv)         45/364 (v)          None of these

(c)    If two balls are randomly drawn from the bag, then what is the probability that either both are Red or Blue ?

(i)                  13/18     (ii)           2 5/91    (iii)          30/91     (iv)         31/91    (v)          None of these

(d)   If three balls are randomly drawn from the bag, then what is the probability that atmost 2 are Green.

(i)                  5/91       (ii)           86/91     (iii)          2 5/51    (iv)         1/24      (v)          None of these

(e)   If three balls are randomly drawn from the bag, then what is the probability that atleast 1 is Red.

(i)                  199/364(ii)           2 5/364 (iii)          1/12       (iv)         1/364    (v)          None of these

(f)     If three balls are randomly drawn from the bag, then what is the probability that none is Blue.

(i)                  3/13        (ii)           7/18       (iii)          2 5/113 (iv)          1/3        (v)          None of these

(g)    If three balls are randomly drawn from the bag, then what is the probability that one is Blue and other 2 are of other than Blue.

(i)                  3/18       (ii)           2 5/18    (iii)          45/91     (iv)         1/4        (v)          None of these

 ANSWERS:

QUES 1

(a)  (i)

(b)  (iii)        

(c)   (iii)

(d)  (iv)

(e)  (i)

QUES 2

(a)  (ii)

(b)  (iv)

(c)   (iii)

(d)  (ii)

(e)  (i)

(f)   (i)

(g)  (iii)

Percentage

Ram spends m% of his income on house hold expenses,n% of the remaining on rent and then he has ` P left. Find his total income ?

                                           

                              REMAINING INCOME  X  100 X 100

TOTAL INCOME = ---------------------------------------------

                                       (100-m) x (100-n)

EXAMPLE :

Ques : Ram spends 40% of his income on house hold expenses, 10% of the remaining on rent and then he has  ` 4050 left. Find his total income ?

Ans :                 

                                                          4050 x 100 x 100

                TOTAL INCOME =    ----------------------------

                                                               60 X 90

                            = ` 7500 

SQUARE

Find the Square of that number in which last digits are 25

425 x 425

                                180                  625
                             4x4=16                fix   
                             4/2 =2
                             16+2=18x10
                                              fix
          Steps :
Step 1 : 625 at end is fix.
Step 2 : Square of 4 = 16
Step 3 : Half of 4      = 2     
Step 4 : Sum of 16 + 2 = 18
Step 5 : Multiply 18 by 10 = 180 and 10 is Fix.