Chapter 2 - Probability

The probability of being depressed is independent of having dark hair. The probability of being depressed is 0.1. The probability of having dark hair is 0.5. The probability that someone has dark hair and is depressed is?

0.05

The probability that first year graduate students complete a PhD program with a doctorate within 10 years is 0.48. This implies that _____ fail to do so.

0.52

The probability that someone is smart is 0.25. The probability that someone is not smart is?

0.75

The probabilities of all outcomes in a sample space add up to

1

Find the matching pairs: (Lack of independence) A. Conditional probability B. Union C. Intersection

A

The probability that someone has blonde hair is 0.2. The probability that someone has an IQ over 115 is 0.15. Assuming that IQ and hair color are independent, what is the probability that someone picked at random is both blond and has an IQ over 115? A. 0.03 B. 0.35 C. 0.15 D. 0.2 E. 0.5

A

You want to do a psychological experiment. On any given day, there is a 30% chance that your participant won't show up. In addition, there is a 10% chance that the stimulus presentation software won't work. There is also a 5% chance that there is a problem with saving the data and a 3% chance that there are other problems like experimenter error. For the sake of simplicity, you can assume that all these events are independent. What is the probability that you will be able to do a successful experiment (be able to record useful data) on any given day? A. 0.58 B. 0.5 C. 1 D. 0 E. 0.68

A

Find the matching pairs: (Addition rule) A. Conditional probability B. Union C. Intersection

B

If events A and B are mutually exclusive, the probability of their union is equal to: A. The probability of A alone B. The probability of A added to the probability of B C. The probability of the union minus the intersection D. The probability of B alone E. Their intersection

B

If there are two candidates running in a political primary and they receive an equal number of votes in a county, the outcome is sometimes decided by a coin toss. What is the chance that one candidate would win all coin tosses if there are a total of 6 of them - assuming that the coins are fair? A. 1 in 6 (16.6%) B. 1 in 64 (1.5%) C. 1 in 32 (3%) D. 1 in 20 (5%) E. 1 in 2 (50%)

B

You are a grand strategist considering a military operation. The success of plan A relies on the following assumptions to be true (which you can assume to be independent): That the enemy doesn't spot you first, which you estimate as 0.9, that there will be artillery support, which you estimate at 0.9, that there will be air support, which you estimate at 0.9, that there will be sufficient fuel for your tanks, which you estimate at 0.9, that all elements of your combined arms effort are coordinating well, which you estimate at 0.9 and that the weather cooperates, which you also estimate at 0.9. Or plan B, which relies on a daring paratrooper drop on the enemy HQ, the success of which you estimate at 0.65. Assuming your estimates are accurate, which of these two plans should you adopt in order to maximize the probability of success of the operation? A. It doesn't matter - the two plans are equally likely to succeed. B. Plan B - simplicity wins the day. C. The optimal course of action cannot be determined from the information given. D. Neither - these are both terrible plans with no realistic chance of success. E. Plan A - these are pretty good chances.

B

You attend the first lecture of a course and estimate the probability that you will get an "A" in this course. The next lecture, you adjust your estimate of getting an "A" based on the content of the 2nd lecture. This process implies which interpretation of probability? A. Frequentist/Objective B. Bayesian/Subjective C. Inductive D. Anecdotal E. Weighted probability

B

Find the matching pairs: (Multiplication rule) A. Conditional probability B. Union C. Intersection

C

The probability of the intersection of A and B is equal to: A. The probability of A times the probability of B B. The probability of A alone C. It can't be determined from this information, it depends on whether A and B are independent or not D. The probability of B alone E. The probability of the union of A and B

C

The probability that someone is drunk at a party is 0.7. The probability that someone is getting into a fight at a party is 0.1. The probability that someone is drunk and getting into a fight is 0.08. What is the probability that someone is getting into a fight if they are drunk? A. 0.8 B. 0.1 C. 0.114 D. 0.7 E. 0.2

C

40% of students live in a dorm and attend lectures remotely. 50% of students attend lectures remotely. What is the probability that a student who is attending lectures remotely lives in a dorm? A. 0.25 B. 0.4 C. 0.2 D. 0.8 E. 0.5

D

An event A is independent of an event B if: A. The probability of A equals the probability of A given B B. The probability of A and B happening must equal zero C. The probability of the intersection of A and B is equal to the probability of A times the probability of B D. Both a) and c) E. Both b) and c)

D

At age 60, there is an equal number of men and women in the population. Schizophrenia is independent of gender* and affects 2% of the population. What is the probability that a randomly picked person from the population is a 60 year old man with schizophrenia?*This is actually not true. It is slightly more common in males. But for the purposes of this exercise, assume it to be independent. A. 0.52 B. 60 C. 0.1 D. 0.01 E. 0.02

D

From empirical studies, we know that the lifetime prevalence for depression is 10%. We also know that the probability of someone being both female and depressed at the same time is 0.07. What is the probability that someone who is depressed is female? A. 0.07 B. 0.5 C. 0.1 D. 0.7 E. 0

D

In a binary world with only two possible and mutually exclusive outcomes A and B, the probability of B can be arrived at by calculating: A. p(B) B. 1-p(A) C. p(~A) D. All of the above E. None of the above

D

The probability of being born male is 0.52. The probability of being born female is 0.48. Assume that someone close to you is pregnant. What is the probability that the child will be either male or female? A. 0.25 B. 0.48 C. 0.52 D. 1 E. 0.1

D

25% of addicts are using both cocaine and heroin. 70% of addicts use cocaine. What is the probability that an addict is using heroin if they are using cocaine? A. 0.25 B. 0.7 C. 0.55 D. 0.5 E. 0.35

E

If events A and B are not mutually exclusive, their combined probability (A happening or B happening) is given by the: A. Probability of A and B minus the probability of A or B B. Intersection C. Probability of A plus the probability of B plus the probability of A and B D. Union E. Probability of A plus the probability of B minus the probability of A and B

E

The probability of the intersection of two independent events A and B can be calculated as: A. p(A)^p(B) B. p(A) - p(B) C. p(A) + p(B) D. p(A) / p(B) E. p(A) * p(B)

E

The probability that someone is drunk at a party is 0.7. The probability that someone is getting into a fight at a party is 0.1. The probability that someone is drunk and getting into a fight is 0.08. What is the probability that someone was drunk if they got into a fight? A. 0.1 B. 0.7 C. 0.114 D. 0.25 E. 0.8

E

The probability that someone's last name starts with a vowel is 0.4. The probability that someone's last name starts with the letter "S" is 0.1. What is the probability that someone's last name either starts with a vowel or the letter S? A. 0.3 B. 0.6 C. 0.4 D. 0.1 E. 0.5

E