Question

1. A box has 4 blue marbles and 3 red marbles. A marble is drawn randomly from the box and its colour was recorded. It is then put into the box. After that, another marble is drawn randomly and its colour was recorded. Calculate the probability both marbles are the same colour.
2. The blood groups of 200 people are distributed as follows: 50 have type A blood, 65 have B blood type, 70 have O blood type and 15 have type AB blood. If a person from this group is selected at random, what is the probability that this person has O blood type?

Answer 1

1)

Total Marbles = 7

Red Marbles=3

So probably of 1st red pull is 3 / 7

As the marble is again returned to the box, probablity of second red pull is also 3 /7

As both of these are mutually exclusive actions, probablity of them occuring together will be 3 / 7 * 3 / 7 = 0.1837

Similarly, Blue Marbles =4

So probably of 1st blue pull is 4 / 7

As the marble is again returned to the box, probablity of second blue pull is also 4 /7

As both of these are mutually exclusive actions, probablity of them occuring together will be 4 / 7 * 4 / 7 = 0.3265

Therefore p ( both marbles same colour) = 0.1837 + 0.3265 = 0.5102

2) Given that, n = 200, O blood group people count = 70

p (person has O blood type) = 70 / 200 = 0.35