Lab Assignment 3.2, 3.3, 3.4
- Page ID
- 36481
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Lab Assignment 3.2, 3.3, 3.4
1. The table below describes the distribution of a random sample S of 100 individuals, organized by gender and whether they are right- or left-handed.
|
Right-handed |
Left-handed |
|
|
Male |
43 |
9 |
|
Female |
44 |
4 |
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)
2. The table below shows a random sample of musicians and how they learned to play their instruments.
|
Gender |
Self-taught |
Studied in School |
Private Instruction |
Total |
|
Female |
12 |
38 |
22 |
72 |
|
Male |
19 |
24 |
15 |
58 |
|
Total |
31 |
62 |
37 |
130 |
- Find P(musician is a female).
- Find P(musician is a male AND had private instruction).
- Find P(musician is a female OR is self taught).
- If three musicians are randomly selected, with replacement, find the probability they are all self-taught.
- If three musicians are randomly selected, without replacement, find the probability they are all males.
- At a college, 72% of courses have a final exam. If we randomly select 5 courses, find the probability that they all have a final exam.
- The casino game, roulette, allows the gambler to bet on the probability of a ball, which spins in the roulette wheel, landing on a particular color, number, or range of numbers. The table used to place bets contains of 38 numbers, and each number is assigned to a color and a range.
- List the sample space of the 38 possible outcomes in roulette.
- You bet on red. Find P(red).
- You bet on -1st 12- (1st Dozen). Find P(-1st 12-).
- You bet on an even number. Find P(even number).
- Is getting an odd number the complement of getting an even number? Why?
3
5. The table below identifies a group of children by one of four hair colors, and by type of hair.
|
Hair Type |
Brown |
Blond |
Black |
Red |
Totals |
|
Wavy |
20 |
15 |
3 |
43 |
|
|
Straight |
80 |
15 |
12 |
||
|
Totals |
20 |
215 |
- Complete the table.
- What is the probability that a randomly selected child will have wavy hair?
- What is the probability that a randomly selected child will have either brown or blond hair?
- What is the probability that a randomly selected child will have wavy brown hair?
- What is the probability that a randomly selected child will have red hair, given that he or she has straight hair?
- If B is the event of a child having brown hair, find the probability of the complement of B.
- If two children are randomly selected with replacement, find the probability that they both have red hair?
- If two children are randomly selected without replacement, find the probability that they both have red hair?