how many outcomes does this experiment have?

Question

For this problem, involving selection of numbered balls from a box, assume the balls in the box are numbered 1 through 8, and that an experiment consists of randomly selecting 2 balls one after another without replacement.

(1) How many outcomes does this experiment have?


(2) What probability should be assigned to each outcome?


(3) What probability should be assigned to the event that at least one ball has an odd number?

Answer 1

The number of outcomes:    8x7=56

 

The probability of each outcome:   1/56

 

The easiest way to find out how many of the total outcomes have at least one odd number is to figure out how many outcomes have only even numbers and subtract that from the total number of outcomes.

 

Number of outcomes with only even numbers (there are only 4 even numbers in the set {1,2,3,4,5,6,7,8}:   4x3=12

 

Number of outcomes with at least one odd number:  56-12=44

 

Probability of at least one odd number:   44/56=11/14