Example 3.3 from Statistics, 3.1 Terminology

Terminology: example 3.3

Let’s denote the events M = the subject is male, F = the subject is female, R = the subject is right-handed, L = the subject is left-handed. Compute the following probabilities:

P(M)
P(F)
P(R)
P(L)
P(M AND R)
P(F AND L)
P(M OR F)
P(M OR R)
P(F OR L)
P(M')
P(R|M)
P(F|L)
P(L|F)

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

1
Solution
1. $P (M) = \frac{number of males}{total number of subjects} = \frac{43 + 9}{43 + 9 + 44 + 4} = \frac{52}{100} = .52$
2. $P (F) = \frac{number of females}{total number of subjects} = \frac{44 + 4}{43 + 9 + 44 + 4} = \frac{48}{100} = .48$
3. $P (R) = \frac{number of right-handed subjects}{total number of subjects} = \frac{43 + 44}{43 + 9 + 44 + 4} = \frac{87}{100} = .87$
4. $P (L) = \frac{number of left-handed subjects}{total number of subjects} = \frac{9 + 4}{43 + 9 + 44 + 4} = \frac{13}{100} = .13$
5. $P (M and R) = \frac{number of male, right-handed subjects}{total number of subjects} = \frac{43}{100} = .43$
6. $P (F and L) = \frac{number of female, left-handed subjects}{total number of subjects} = \frac{4}{100} = .04$
7. $P (M or F) = \frac{number of subjects that are male or female}{total number of subjects} = \frac{52 + 48}{100} = \frac{100}{100} = 1$
8. $P (M or R) = \frac{number of subjects that are male or right-handed}{total number of subjects} = \frac{43 + 9 + 44}{100} = \frac{96}{100} = .96$
9. $P (F or L) = \frac{number of subjects that are female or left-handed}{total number of subjects} = \frac{44 + 4 + 9}{100} = \frac{57}{100} = .57$
10. $P (M^{'}) = \frac{number of subjects who are not male}{total number of subjects} = \frac{44 + 4}{43 + 9 + 44 + 4} = \frac{48}{100} = .48$
11. $P (R | M) = \frac{P (R and M)}{P (M)} = \frac{0.43}{0.52} ˜ =.8269$ (rounded to four decimal places)
12. $P (F | L) = \frac{P (F and L)}{P (L)} = \frac{0.04}{0.13} ˜ =.3077$ (rounded to four decimal places)
13. $P (L | F) = \frac{P (L and F)}{P (F)} = \frac{0.04}{0.48} ˜ =.0833$ (rounded to four decimal places)

How did it go?

Solution

Solution