Question

Suppose that a ball is selected at random from an urn with balls numbered from 1 to 100, and without replacing that ball in the urn, a second ball is selected at random. What is the probability that:

1. The sum of two balls is below five.

2. Both balls have odd numbers.

3. Two consecutive numbers ar chosen, in ascending order

Answer 1

There are balls number from 1 to 100. Number of ways in which 2 balls can be picked =

1. Cases where the two balls sums below 5 =

(1,3) ; (2,2) ; (3,1) ; (1,2) ; (2,1) ; (1,1)

Number of ways the two balls sums up to 5

= 6

P(Number of ways the two balls sums up to 5) =

2. Number of cases where both the balls are odd numbers =

P(Both balls have odd numbers)

3. Number of cases where two consecutive numbers are chosen (in ascending order)

= 99

P(Two consecutive numbers ar chosen, in ascending order)