SOLUTION: Good evening, I'm having a hard time understanding this problem if anyone can help me it would be greatly appreciated 1)Use the contingency table below to compute the following

Question 871010: Good evening, I'm having a hard time understanding this problem if anyone can help me it would be greatly appreciated
1)Use the contingency table below to compute the following probabilities, based on a random sample of a subject:
a) P(Male/ Basketball)
b) P(Female or Baseball)
c) P(Football)
d) P(Male and Football)
Prefer to
watch on TV
Gender Baseball Basketball Football Total
Male 70 60 50 180
Female 50 40 30 120
Total 120 100 80 300

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1)Use the contingency table below to compute the following probabilities, based on a random sample of a subject:

a) P(Male | Basketball)

This is saying "Probability of picking a male given s/he likes basketball"

Look in the basketball column. There are 100 people total here. There are 60 of them who are male, so 60/100 = 6/10 = 3/5 is the probability

P(Male | Basketball) = 3/5
----------------------------------------------------
b) P(Female or Baseball)

There are 120 females total (see the "total" in the "female" row).
There are 120 baseball fans total (see the "total" in the "baseball" column).
There are 50 baseball fans who are female (intersection of female row and baseball column)

So there are 120+120-50 = 240-50 = 190 people who either are female or like baseball (or are both female and like baseball). We subtract off that 50 because of the double counting.

So we have 190 people of what we're looking for out of 300 total people (bottom right corner). Divide the two: 190/300 = 19/30

P(Female or Baseball) = 19/30
----------------------------------------------------
c) P(Football)

There are 80 total football fans (male + female)

This is out of 300 people total

80/300 = 8/30 = 4/15

P(Football) = 4/15

----------------------------------------------------
d) P(Male and Football)

There are 50 males who happen to like football as well. This is out of 300 people total.

50/300 = 1/6

P(Male and Football) = 1/6
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