Question

A box contains

11

balls numbered 1 through

11.

Two balls are drawn in succession without replacement. If the second ball has the number 4 on​ it, what is the probability that the first ball had a smaller number on​ it? An even number on​ it?

The probability that the first ball had a smaller number is

_____.

​(Type a fraction. Simplify your​ answer.)

The probability that the first ball had an even number is

____.

​(Type a fraction. Simplify your​ answer.)

Answer 1

(a) To find the probability that the first ball had a smaller number:

Total number of balls = 11

Total number of balls smaller than 4 is 3(1,2 and 3)

Second ball already selected and it has the number 4 on it

So remaining balls = 10

Now the probability that the first ball had a smaller number = 3/11

Now the probability that the first ball had a smaller number = 0.2727

Therefore the probability that the first ball had a smaller number is 0.2727

(b) To find the probability that the first ball had an even number:

Total number of balls = 11

Total number of even numbers from 1 to 11 is 5 those are 2,4,6,8,10

The number of 4 is even number

So Remaining even numbers = 4

Remaining balls = 10

Now the probability that the first ball had an even number = 4/ 10

The probability that the first ball had an even number = 0.4

Therefore the probability that the first ball had an even number is 0.4