The table below shows which hand is favored by each of 100 people (50 men and 50 women). Determine the probability that someone selected randomly from the...

Question

The table below shows which hand is favored by each of 100 people (50 men and 50 women). Use the information in the table to determine the probability that someone selected randomly from the group will be female or left-handed.

           Left-Handed Right-Handed
Men     25         25
Women 15        35

Answer 1

This can be solved by looking at the table and adding up the appropriate categories:

 

number of female or left-handed =

   50 females + 25 left-handed males.

so, prob = 0.75 or 75%.

 

A more mathematical way to get this is to use the formula for combining probabilities with an "or" condition:

 

  p(A or B) = p(A) + p(B) - p(A and B)

 

If A and B are mutually exclusive then the last term is zero and we just add the probabilities.

But if there is overlap between A and B, then that overlap is double counted by adding the probabilities, so we subtract one overlap probability, the "- p(A and B)" term.

 

For the example here:

prob female = 50%

prob left handed = 40%

prob female and left-handed: 15%

so

 prob female or left-handed = 50% + 40% - 15% = 75%.