Names: Sam G., Alex N., Albert S., and Noushyar E.
3.1-3.3 Review
1. There are 16 students total. 12 of the students take math and 8 of the students take science.
Find how many students take both math and science if only one student does not take math or
science?
2. The two events X and Z are such that P(X)=0.6, P(Z)= 0.2 and P(X|Z)=0.1
Calculate the probabilities that:
a. Both of the events occur
b. At least one of the events occur
c. Exactly one of the events occur
3.4
3. There are 27 students in a class. 15 take Art and 20 take Theater. Four do neither subject.
How many students do both subjects?
One person is chosen at random. Find the probability that
a. he or she takes Theater but not Art
b. he or she takes at least one of the two subjects
c. he or she takes Theater, given that he or she takes Art
4. For events A and B, it is known that the probability of A’ and B’ is equal to 0.35. The
probability of A is equal to 0.25 while the probability of B is equal to 0.6. Find
a. Probability of A and B
b. Probability of A given B
c. Probability of B’ given A’
Chapter 3 Review
5. A bag contains 6 red apples and 10 green apples. Without looking into the bag, Maddy
randomly selects one apple.
a. What is the probability it is red?
The apple is red and Maddy eats it. Next the bag is passed to Janet. Without looking into
the bag, she randomly selects one apple.
b. What is the probability that it is green?
The apple is green and Janet replaces it in the bag. Next the bag is passed to Tarish.
Without looking into the bag, he randomly selects two apples.
c. What is the probability that they are both red?
8.5
6. Find the missing frequency, K, and the interquartile range of the given table. The total
frequency is 100 Graph the cumulative frequency to help you with the problem.
Number
1
2
3
4
5
6
Frequency(f) 26
10
20
K
29
11
7. Show this data on a cumulative frequency diagram.
Age (years) Frequency
10
3
11
18
12
13
13
12
14
7
15
27
a. Estimate the median
b. Estimate the interquartile range
15.2
1
8. X is binomially distributed with 4 trials and a probability of success equal to 2 on each trial.
Without a calculator determine the probability of:
a. P(X=1)
b. P(X< 1)
c. P(X≤ 1)
d. P(X≥ 1)
9. A regular tetrahedron has three white faces and one red face. It is rolled four times and the
color the bottom face is noted. What is the most likely number of times that the red face will
end downwards? What is the probability of this value occurring?
10. The probability that Nicole goes to bed at 7:30 on a given day is 0.4. Calculate the
probability that on five consecutive days she goes to bed at 7:30 on at most three days.
15.3
11. Find the area under the standard normal curve
a. between 1 and 2 standard deviation from the mean.
b. between 0.5 and 1.5 standard deviations from the mean.
12. The lengths of sticks at a stick shop are normally distributed with mean μ and standard
deviation 7 cm. if 2.5% of the sticks measure more than 68 cm find the value of μ.
Previous Chapters
13. Determine the following limit: lim
ℎ→0
𝜋
6
𝜋
6
tan( +ℎ)−tan
ℎ
14. Find the derivative of the function 𝑓(𝑥) = 3 sin2 (𝑒 2𝑥 ) and simplify your answer.
15. When 𝑓(𝑥) = −𝑥 3 − 9𝑥 2 + 17 find the following.
a. Use the Second Derivative Test to find where the extrema of the function occur.
b. Find the intervals in which the function is increasing and decreasing.
c. Determine where the function is concave up and where it is concave down, and find
(if any) points of inflection.
16. Integrate from u(a) to u(b).
1
∫ √t 5 + 2t (5t 4 + 2) dt
0
17. Find the Volume of y = x 2 as it is rotating around the x-axis between x = 0 and x = 3.
Solutions
1. (12 − 𝑥) + (8 − 𝑥) + 𝑥 + 1 = 16
21 − 𝑥 = −5
𝑥=5
5 students take both math and science
2. 𝑋 ∩ 𝑍 = 0.1 ∗ 0.2 = 0.02
𝑋 ∪ 𝑍 = 0.78
𝑃(𝑋 ∪ 𝑍) − 𝑃(𝑋 ∩ 𝑍) = 0.76
1
𝑃(𝑍|𝑋) =
30
3. 12 take both subjects
a. 8/27
b. 23/27
c. 0.8
4. a. 0.2
b. ⅓
c. 7/15
5. a) P(A∩𝑩)= 0.02 b) P(A∩𝑩)=0.78 c) P(A∩𝑩)−𝐏(𝐀∪𝑩)=𝟎.𝟕𝟔
6. 26+10+20+29+11= 96
100-96=4, K=4
IQR= 4.5=0.9
= 3.6
7.
1
1
5
15
8. a) 4 b) 16 c) 16 d) 16
9. 1; 0.421
10. 0.913
11. Parts
a. 0.272
b. 0.483
12. 54.3 cm
4
13. 3
14. 6e2xsin2e2x
15. Parts
a. Max: x = 0, min: x = 6
b. x < - 6, 0 < x
c. Up: x < -3, down: x > -3
16. 4√3
243
17. 5 π units cubed