STAT 245 Lecture Notes - Lecture 3: Mutual Exclusivity
STAT 245.3 – Exercises #3
Solutions
PROBLEM A: How physically active are students? A random sample of students was obtained
by sampling student numbers from a list of such numbers for current students. Each student
indicated a Level of Physical Activity and his/her Gender. The following table summarizes
the results obtained.
Level of Physical Activity
Gender/Sex
Low
Medium
High
Totals
Female
220
402
302
924
Male
180
318
258
756
Totals
400
720
560
1680
Suppose one person is chosen at random from those studied. For questions 1 to 6, determine the
probabilities that the person so chosen: (Note: Show how you calculate your answers using the
numbers given in the above table, then present answers correct to four places of decimal.)
Let 𝐹 denote Female,
𝐹𝐶 denote Male,
𝐿 denote Low activity level,
𝑀 denote Medium activity level
And 𝐻 denote High activity level.
1. is a female with High activity level
𝑃(𝐹 ∩ 𝐻)=302
1680 =151
840 ≈ 0.1798
2. is not a "female with high activity"
𝑃((𝐹 ∩ 𝐻)𝐶)= 1 − 151
840 =689
840 ≈ 0.8202
3. is a male or has Medium activity level
𝑃(𝐹𝐶∪ 𝑀)=756 +720 −318
1680 =1158
1680 =193/280 ≈ 0.6893
4. does not have a High activity level
𝑃(𝐻𝐶)= 1 − 560
1680 =1120
1680 =2
3≈ 0.6667