Probability (Medium Level) - CAT MCQ

The possible outcomes are:
 (1, 1); (1, 2); (2, 1), (2, 2); (3, 1); (1, 3).
Out of six cases, in two cases there is exactly one ‘2’
Thus, the correct answer is 2/6 = 1/3.

The event can be defined as:
The first bag is selected and a red ball is drawn.
 or a second bag is selected and a red ball is drawn.
1/2 X 5/12 + 1⁄2 X 3/15 = (5/24) + (3/30) = 37/120

For the greatest chance of drawing a red ball the distribution has to be 1 Red in the first bag and 4 red + 12 white balls in the second bag. This gives us
½ X 1+½ X 4/16 =5 / 8 

A leap year has 366 days – which means 52 completed weeks and 2 more days. The last two days can be (Sunday, Monday) or (Monday, Tuesday) or ....... (Saturday, Sunday).2 scenarios out of 7 have a 53rd Sunday. Thus, 2/7 is the required answer

Blue and Red or Red and Blue
= (10/25) X (15/24) + (15/25) X(10/24) = (1/2). 

Required probability = probability of first die shows a composite number x probability of second die shows an odd number x probability of third die shows an odd prime number 
= 2/6 X 3/6 X 2/6 = 1/18.

Girl and Boy and Boy or Boy and Girl and Boy Or Boy and Boy and Girl
= (3/4) X(2/4) X(2/3) + (1/4) X(2/4) X(2/3) + (1/4) X(2/4) X(1/3) = 18/48 = 3/8.

The event definition here is that first is not a heart and second is not a heart and third is a heart = (3/4) X(3/4) X (1/4) = 9/64

 P = Total no of ways in which two people sit together / Total No. of way
= (10! X 2!)/11!
= 2/11

The required probability = (Probability of drawing any ball from the bag as the first ball). (Probability of drawing a blue ball from it as the second ball)
= 6/18 = 1/3