Question

math 120 exam 2 review: chapters 5 - 7

1. (5.5) how many different 10 - letter words (real or imaginary) can be formed from the following letters? z, v, p, e, z, v, p, a, z
2. a university conducted a survey of 390 undergraduate students regarding satisfaction with student government. results of the survey are shown in the table by class rank.

	freshman	sophomore	junior	senior	total
neutral	25	10	14	11	60
not satisfied	23	17	20	28	88
total	105	82	100	103	390

(a) (5.2) if a survey participant is selected at random, what is the probability that he or she is a junior?
(b) (5.2) if a survey participant is selected at random, what is the probability that he or she is satisfied or a junior?
(c) (5.4) if a junior is selected at random, what is the probability that he or she is satisfied?

Explanation:

Step1: Identify total number of students

The total number of survey - participants is 390.

Step2: Calculate probability of being a junior

The number of juniors is 100. The probability $P(\text{junior})$ of selecting a junior is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P(\text{junior})=\frac{100}{390}=\frac{10}{39}\approx0.2564$.

Step3: Calculate number of satisfied or junior students

The number of satisfied students is 242 and the number of juniors is 100, and the number of satisfied juniors is 66. Using the formula $P(A\cup B)=P(A)+P(B)-P(A\cap B)$, the number of satisfied or junior students is $242 + 100-66=276$. Then the probability $P(\text{satisfied or junior})=\frac{276}{390}=\frac{46}{65}\approx0.7077$.

Step4: Calculate probability of being satisfied given junior

The number of satisfied juniors is 66 and the number of juniors is 100. Using the formula for conditional probability $P(\text{satisfied}|\text{junior})=\frac{\text{Number of satisfied juniors}}{\text{Number of juniors}}$, we get $P(\text{satisfied}|\text{junior})=\frac{66}{100}=0.66$.

Answer:

(a) $\frac{10}{39}\approx0.2564$
(b) $\frac{46}{65}\approx0.7077$
(c) $0.66$