Download Statistics/Probability Activity sheet

Statistics/Probability Activity sheet
1.
Three employees work in a small engineering firm. The probabilities of them each
being absent on any particular day are 0.1, 0.04, 0.05. If all employees are absent on
the day, the firm will shut down for that day. It is also known that any employee being
absent on any particular day is independent of whether or not the others are absent.
Calculate the probability that on any particular day
(1) all employees are present,
(ii) the firm will shut down,
(iii) only one employee is absent,
(iv) only two employees are absent,
(v) all three employees are absent, and
(vi) at least one employee is absent.
2. Three candidates A, B, and C are seeking public office. Candidates A and B are
given the same chance of winning. Candidate C is given twice the chance of either A
or B of winning. What is the probability that
(a) A wins
(b) C wins
(c) B does not win?
3. The probabilities that a stockbroker will invest in tax-free bonds, mutual funds,
tax-free and mutual funds are respectively, 0.6, 0.3, and 0.15. Find the probability that
the stock broker will invest in:
a) either tax-free bonds or mutual funds.
b) neither tax-free bonds or mutual funds.
4. In a certain federal prison, 2/3 of the inmates are under 25 years of age, 3/5 are
male, and 5/8 are female or 25 years of age or older. Find the probability of selecting
an inmate who is female and at least 25 years old.
5. The following probabilities apply to the numbers of patients waiting in a hospital
emergency room at any specific time:
Number of patients waiting 0
1
2
3
4
5 or more
-------------------------------------------------------------------------------------Probability
.34 .28 .13 .11 .08
.06
Find the probability that:
a) 2 or fewer are waiting.
b) 4 or more are waiting.
c) at least one patient is waiting.
6. The odds in favour of an event E are quoted as a to b if and only if
P( E ) 
a
( a  b)
a) An insurance company quotes odds of 3 to 1 for the event that an individual 70
years of age will survive another 10 years. What is the probability assigned to this
event?
b) If the probability of a successful transplant operation is 1/8, what are the odds
against this type of surgery?
7. A town has two fire engines operating independently. The probability that a specific
fire engine is available when needed is 0.96. What is the probability that:
a)
both fire engines are not available?
b)
a fire engine is available when needed?
8. A purchasing agent has placed two orders for a particular raw material from two
different suppliers A and B. If neither order arrives in two weeks the production
process will be shut down until at least one of the orders arrives. The probability that
supplier A can deliver the material in 2 weeks is 0. 40. The probability that supplier B
can deliver the material in 2 weeks is 0.50. Find the probability that:
a)
both suppliers deliver the material in 2 weeks.
b)
at least one supplier delivers the material in 2 weeks.
c)
the production process is shut down in 2 weeks time because both
orders are late.
9. A marketing research company is studying the brand loyalty behaviour of the
consumers of its product, brand B. Studies indicate that the consumers as a group have
a rather fixed pattern of behaviour with respect to choosing an alternative brand in
repeated purchases. Suppose that 60% of brand A buyers repurchase brand A the next
time they buy and that 70% of brand B buyers repurchase brand B the next time they
buy. Assume that everyone buys either brand A or brand B and that the frequency of
buying is the same for both. What is the probability that a randomly selected customer
will buy brand A in the next purchase if initially brands A and B divided the market
equally?
10. There are 40 students taking courses in one or more of economics, statistics, and
accountancy: out of those, 20 are taking accountancy, 20 are taking economics, 10 are
taking statistics and economics, 10 are taking economics and accountancy, 5 are taking
all three subjects and 8 are taking accountancy only. One student is selected at random.
Find the probability that the student will be taking:
a)
b)
c)
d)
statistics only.
statistics and accountacy.
either accountancy or economics.
all three subjects.
ANSWERS
1.
(i)
(ii)
(iii)
(iv)
(v)
(vi)
0.9*0.96*0.95 = 0.8208
0.1*0.04*0.05 = 0.0002
0.1*0.96*0.95 + 0.9*0.04*0.95 + 0.9*0.96*0.05
0.1*0.04*0.95 + 0.9*0.04*0.05 + 0.1*0.96*0.05
same as (ii) !!
1-P(None absent) = 1-P(All present) = 1-0.9*0.96*0.95 = 0.1792
2.
(a)
1/4
(b) 1/2
(c) 3/4
3.
(a) 0.75
4.
P(F or >25) = P(F) + P(>25) - P(F and >25)
5/8
= 2/5 + 1/3 - P(F and >25)
P(F and >25) = 2/5 + 1/3 - 5/8
= (48 + 40 - 75)/120 = 13/120
5.
(a) 0.75
6.
P(E) = a/(a + b) = 3/4 = 0.75
P(E) = a/(a + b) = 1/8 = 1/(1 + 7)
7 to 1
7.
(a) P(A and B) = 0.0016
(b) 0.9984
8.
(a) 0.4 x 0.5 = 0.2
(b)1 - (0.6 x 0.5) = 0.7
9.
P(A2|A1) = 0.6,
(b) 0.25
(b) 0.14
(c) 0.66
P(B2|B1)= 0.7,
P(A1) = P(B1) = 0.5.
P(A2) = P(A2A1) + P(A2B1)
= P(A1) P(A2|A1) + P(B1) P(A2|B1)
= 0.5 (0.6) + 0.5 (0.3) = 0.3 + 0.15 = 0.45
10.
(a) P(S only) = 10/40 = 0.25
(b) P(S and A) = 7/40 = 0.175
(c) P(E or A) = 30/40 = 0.75
(d) P(S and E and A) = 5/40 = 0.125
(c) 0.3