How do you answer this question?

enter image source here

1 Answer
Feb 1, 2018

# (a) :40, (b) : 1/16#.

Explanation:

Let, #M, and N# be the events that the chocolate selected

from the Box is a Milk one, and contains Nuts, resp.

Then, #M'# denotes the event that the chocolate selected is

not a milk chocolate.

To determine #P(M) :#

There are #(3x+4)+x+(x-2)+(2x+3)=(7x+5)#

chocolates in the box, out of which #1# chocolate can be selected in

#(7x+5)" ways"#.

No. of milk chocolates is #(3x+4)+x=(4x+4)#, so, #1# can be

chosen in #(4x+4)" ways"#.

#:. P(M)=(4x+4)/(7x+5)..................................(square_1)#.

Similarly, #P(N)=(2x-2)/(7x+5)...............................(square_2)#.

Given taht, #P(M)=3P(N) rArr (4x+4)/(7x+5)=3((2x-2)/(7x+5))#.

#rArr 4x+4=6x-6 rArr 10=2x, i.e., x=5#.

Part (a) :

#"No. of chocolates in the Box"=7x+5=7*5+5=40#.

Part (b) :

#"The Reqd. Prob.="(P(N))/(P(M'))#,

#=(P(NnnM'))/(P(M'))#,

#=(P(N)-P(NnnM))/(1-P(M))#,

#={(2x-2)/(7x+5)-x/(7x+5)}-:{1-(4x+4)/(7x+5)}#,

#=(x-2)/(3x+1)=(5-2)/(3*5+1)......[because, x=5]#.

#rArr "The Reqd. Prob.="1/16#.

Enjoy Maths., and, Spread the Joy!