Download THEME THREE

Seminar 1 Probability
1. If there were 12 cloudy days during a 30-day period, what was the relative
frequency of the cloudy day?
2. A nurse notes that on one day 23 out of 50 new patients had a fever, while
on another day 28 out of 56 had a fever. The two relative frequencies for two
days are different. Does it contradict to the law of large numbers?
3. If the probability that a company will win a contract is 0.3, what is the
probability that it will not win the contract?
4. Suppose the probability that the worker of a certain factory is a smoker is
0.4. What is the probability that in a company of two workers, chosen at
random, are a) exactly 2 smokers, b) exactly 1 smoker, c) at least 1 smoker, d)
no smoker
5. If the probabilities that Jane, Tom, and Mary will be chosen chairperson of
the board are 0.5, 0.3, and 0.2, respectively, what is the probability that the
chairperson will be either Jane or Mary?
6. Suppose the probability that a construction company will be awarded a
certain contract is 0.25, the probability that it will be awarded a second contract
is 0.21, and the probability that it will get both contracts is 0.13. What is the
probability that the company will win at least one of the two contracts?
7. The probability that a student will receive a state grant is
1
, while the
3
1
. If whether or not she
2
receives one grant is not influenced by whether or not she receives the other,
what is the probability of her receiving both grants? No grant? At least one?
probability that she will be awarded a federal grant is
8. Suppose a reputed psychic in an extrasensory perception (ESP) experiment
has called heads or tails correctly on ten successive tosses of a coin. What is
the probability that guessing would have yielded this perfect score?
9. The table below gives the results of a survey of the drinking and smoking
habits of 1200 college students. Rows and columns have also been summed.
Smoke
Drink
beer
315
Don't
drink
165
480
Don't smoke
585
135
720
900
300
1200
a. What is the probability that someone in this group smokes?
b. What is the probability a student smokes given that she is a beer drinker?
c. What is the probability that someone drinks?
d. What is the probability that students drink given that they smoke?
10. If 90% of the households in a certain region have answering machines and
50% have both answering machines and call waiting, what is the probability
that a household chosen at random and found to have an answering machine
also has call waiting?
11. A psychologist interested in right-handedness versus left-handedness and in
IQ scores collected the following data from a random sample of 2000 high
school students.
High IQ
Righthanded
190
Lefthanded
10
200
Normal IQ
1710
90
1800
1900
100
2000
a. What is the probability that a student from this group has a high IQ?
b. What is the probability that a student has a high IQ given that she is lefthanded?