8) an urn contains balls numbered 1 through 9. a ball is drawn and replaced, and a second ball is drawn. a) describe the outcome "ball number 2
is drawn, then ball number 7 is drawn."
b) how many outcomes are in the sample space?
a) describe the outcome "ball number
2 is drawn, then ball number 7 is drawn."
b) how many outcomes are in the sample space?

Answer and Explanation:

Given : An urn contains balls numbered 1 through 9. A ball is drawn and replaced, and a second ball is drawn.

To find : a) Describe the outcome "ball number 2  is drawn, then ball number 7 is drawn."

b) How many outcomes are in the sample space?

Solution :

a) An urn contains balls numbered 1 through 9 i.e. 1,2,3,4,5,6,7,8,9.

Total number of outcomes = 9

Favorable outcome of getting first ball number 2 is drawn is 1.

Probability of getting first ball number 2 is

A ball is drawn and replaced, and a second ball is drawn.

Favorable outcome of getting second ball number 7 is drawn is 1.

Probability of getting second ball number 7 is

So, Probability of ball number 2  is drawn, then ball number 7 is drawn is

This means When ball number 2 is drawn from 9 ball is 1/9 and as balls is replaced then ball number 7 is drawn from 9 balls is same as 1/9.

b) Number of outcomes in the sample space is {1,2,3,4,5,6,7,8,9}.