An urn contains 2 red marbles and 3 blue marbles. 1. one person takes two marbles at random from the urn and does not replace them. a) state the general ways in which the person could get a red marble and a blue marble b) state the number of ways this can occur. c) what is the probability the person gets a red and a blue marble? p(r & b) =

Given : An urn contains 2 red marbles and 3 blue marbles.

Total marbles = 2+3=5

a) The general ways in which the person could get a red marble and a blue marble are :

1)  He draws red marble first and then second marble as blue.

2)  He draws blue marble first marble and then second marble as red.

b)  The number of ways to get one red and one blue marble is given by :-

                         (i)

c) Number of ways to get 2 marbles from 5 is given by :-

    (ii)

Now, The probability the person gets a red and a blue marble will be :-

      [Divide (i) by (ii)]

Hence, the  probability the person gets a red and a blue marble= 0.6

solution:

the given function is ,

      =

the three roots of this quadratic function is , 0 ,8 and 10.all the roots are real and rational.

if a quadratic equation is of the form ,

sum of the roots = a + b +c= 0+8+10=18=  

product of roots taken two at a time = a b + b c+ c a = 0+80+0=80 =  

product of roots = a b c = 0=  

there are 11 doors in a hall starting from 0 to 11.the entry in the hall is permitted through gate number 0 and exit is allowed through only gate number 8 and 10.so, three roots(0,8,10) of quadratic function is given by entry and exit route of this hall.