STATISTICS FINAL EXAMINATION TEST
COMPLETE QUESTIONS AND SOLUTIONS
◉ If A and B are mutually exclusive, explain why it would be
impossible for P(A) = 0.5 and P(B) = 0.7.
Answer: This is impossible since P(AuB) would be 1.2 for this case
and we know probabilities cannot be greater than 1.
◉ Suppose that P(A') = 0.4, P(B'/A) = 0.3, and P(B'/A') = 0.7. Find
P(A), P(B/A), , and P(B).
Answer: P(A) = 0.6, P(B/A) = 0.7, P(A' n B') - 0.28, P(B) = 0.54
◉ Suppose that P(A) = 0.5, P(B/A) = 0.2, P(B/A') = 0.9. Find P(A'),
P(B'/A'), , and P(B).
Answer: P(A') = 0.5, P(B'/A') = 0.1, P(A n B') = 0.4, P(B) = 0.55
◉ Suppose that you own two factories. Factory I produces 90% of
your output and only 2% of their products are defective. It is also
known that 5% of the parts produced by factory II are defective.
Find the probability that a part produced by your company is
defective. Find the probability that it is not defective.
Answer: P(D) = 0.023, P(D') = 0.977
◉ Suppose that 40% of the population gets a flu vaccination. Of
the people receiving the shot, only 5% get the flu. Of those not
,getting the shot, 40% get the flu. Find the probability that a
person picked at random will get the flu.
Answer: P(F) = 0.26
◉ Compute C(6,2). Explain precisely what your answer
represents.
Answer: C(6,2) = 15 means that there are 15 ways to choose 2
items from a group of 6 items where order does not matter.
◉ Compute C(6,4)
Answer: 15
◉ Comment on any similarities between problems 1 and 2
Answer: C(6,2) = C(6,4). Notice that 6-2 = 4 and 6-4 = 2. This is a
trick for understanding when two
◉ Compute C(3, 0). Explain what your answer represents.
Answer: C(3,0) = 1 since there is only one way to choose 0 items
from a group of 3 things. Just don't take any of them!
◉ Compute C(8,1). Why does the answer equal eight?
Answer: C(8,1) = 8 since there are exactly 8 ways to choose 1 item
from a group of 8 items.....take the first item, or the second, or the
third.....etc.
, ◉ Compute C(7,1) C(4,3) [Hint: This notation means that you
should multiply your answer for C(7,1) times your answer for
C(4,3) ]
Answer: C(7,1) C(4,3) = 7x4 = 28
◉ Verify that the following tables represent probability
distributions. Then find the mean, variance and standard
deviation for each probability distribution.
x P(x)
0 0.92
1 0.03
2 0.03
3 0.02
Answer: μ=0.15,σ^2=0.3075,σ=0.55
◉ Directions: Verify that the following tables represent
probability distributions. Then find the mean, variance and
standard deviation for each probability distribution.
x P(x)
1 0.4
2 0.3
3 0.2
COMPLETE QUESTIONS AND SOLUTIONS
◉ If A and B are mutually exclusive, explain why it would be
impossible for P(A) = 0.5 and P(B) = 0.7.
Answer: This is impossible since P(AuB) would be 1.2 for this case
and we know probabilities cannot be greater than 1.
◉ Suppose that P(A') = 0.4, P(B'/A) = 0.3, and P(B'/A') = 0.7. Find
P(A), P(B/A), , and P(B).
Answer: P(A) = 0.6, P(B/A) = 0.7, P(A' n B') - 0.28, P(B) = 0.54
◉ Suppose that P(A) = 0.5, P(B/A) = 0.2, P(B/A') = 0.9. Find P(A'),
P(B'/A'), , and P(B).
Answer: P(A') = 0.5, P(B'/A') = 0.1, P(A n B') = 0.4, P(B) = 0.55
◉ Suppose that you own two factories. Factory I produces 90% of
your output and only 2% of their products are defective. It is also
known that 5% of the parts produced by factory II are defective.
Find the probability that a part produced by your company is
defective. Find the probability that it is not defective.
Answer: P(D) = 0.023, P(D') = 0.977
◉ Suppose that 40% of the population gets a flu vaccination. Of
the people receiving the shot, only 5% get the flu. Of those not
,getting the shot, 40% get the flu. Find the probability that a
person picked at random will get the flu.
Answer: P(F) = 0.26
◉ Compute C(6,2). Explain precisely what your answer
represents.
Answer: C(6,2) = 15 means that there are 15 ways to choose 2
items from a group of 6 items where order does not matter.
◉ Compute C(6,4)
Answer: 15
◉ Comment on any similarities between problems 1 and 2
Answer: C(6,2) = C(6,4). Notice that 6-2 = 4 and 6-4 = 2. This is a
trick for understanding when two
◉ Compute C(3, 0). Explain what your answer represents.
Answer: C(3,0) = 1 since there is only one way to choose 0 items
from a group of 3 things. Just don't take any of them!
◉ Compute C(8,1). Why does the answer equal eight?
Answer: C(8,1) = 8 since there are exactly 8 ways to choose 1 item
from a group of 8 items.....take the first item, or the second, or the
third.....etc.
, ◉ Compute C(7,1) C(4,3) [Hint: This notation means that you
should multiply your answer for C(7,1) times your answer for
C(4,3) ]
Answer: C(7,1) C(4,3) = 7x4 = 28
◉ Verify that the following tables represent probability
distributions. Then find the mean, variance and standard
deviation for each probability distribution.
x P(x)
0 0.92
1 0.03
2 0.03
3 0.02
Answer: μ=0.15,σ^2=0.3075,σ=0.55
◉ Directions: Verify that the following tables represent
probability distributions. Then find the mean, variance and
standard deviation for each probability distribution.
x P(x)
1 0.4
2 0.3
3 0.2
