Question

1. 100 employees of a company are asked how they get to work and whether they work full time or part time. the figure below shows the results. if one of the 100 employees is randomly selected, find the probability of getting someone who carpools, someone who cycles to work, or someone who works part time.

pie chart with 1,2,3,4

1. public transportation: 10 full time, 8 part time
2. bicycle: 4 full time, 5 part time
3. drive alone: 33 full time, 25 part time
4. carpool: 7 full time, 8 part time

a) 0.44 b) 0.7 c) 0.57 d) 0.24

1. a card is drawn from a well - shuffled deck of 52 cards. find p(drawing a face card or a 4).

a) 16 b) \\(\frac{2}{13}\\) c) \\(\frac{12}{13}\\) d) \\(\frac{4}{13}\\)

1. a bag contains 6 red marbles, 3 blue marbles, and 1 green marble. find p(not blue).

a) \\(\frac{3}{10}\\) b) \\(\frac{7}{10}\\) c) \\(\frac{10}{7}\\) d) 7

1. the probability that an event will occur is 0.3. what is the probability that the event will not occur?

a) \\(\frac{3}{7}\\) b) 0.7 c) 0 d) none of the above is correct.

1. a manufacturing process has a 70% yield, meaning that 70% of the products are acceptable and 30% are defective. if three of the products are randomly selected, find the probability that all of them are acceptable.

a) 0.429 b) 0.027 c) 2.1 d) 0.343

1. a bin contains 64 light bulbs of which 10 are defective. if 5 light bulbs are randomly selected from the bin with replacement, find the probability that all the bulbs selected are good ones. round to the nearest thousandth if necessary.

a) 0 b) 0.844 c) 0.428 d) 0.484

Explanation:

Question 7

Step1: Count carpool, bicycle, part - time

• Carpool: \(7 + 8=15\)
• Bicycle: \(4 + 5 = 9\)
• Part - time: Total part - time employees: Public transportation part - time (\(8\))+ Bicycle part - time (\(5\))+ Drive alone part - time (\(25\))+ Carpool part - time (\(8\))=\(8 + 5+25 + 8=46\)
• But we have double - counted the part - time employees in carpool and bicycle. So we use the principle of inclusion - exclusion. Let \(A\) be carpool, \(B\) be bicycle, \(C\) be part - time.

\(n(A)=15\), \(n(B) = 9\), \(n(C)=46\)
\(n(A\cap C)\): Carpool part - time \(= 8\)
\(n(B\cap C)\): Bicycle part - time \(= 5\)
\(n(A\cap B\cap C)\): Carpool and bicycle and part - time \( = 0\) (since a person can't carpool and bicycle at the same time)
\(n(A\cup B\cup C)=n(A)+n(B)+n(C)-n(A\cap C)-n(B\cap C)+n(A\cap B\cap C)\)
\(n(A\cup B\cup C)=15 + 9+46-8 - 5+0=57\)

Step2: Calculate probability

The total number of employees \(N = 100\). The probability \(P=\frac{n(A\cup B\cup C)}{N}=\frac{57}{100}=0.57\)

Step1: Count face cards and 4s

• Face cards: In a deck, there are 12 face cards (4 Jacks, 4 Queens, 4 Kings)
• Number of 4s: 4 (one 4 in each suit)
• Since face cards and 4s are mutually exclusive (a card can't be a face card and a 4 at the same time), the number of favorable outcomes \(n = 12 + 4=16\)
• Total number of cards \(N = 52\)

Step2: Calculate probability

The probability \(P=\frac{n}{N}=\frac{16}{52}=\frac{4}{13}\)

Step1: Total number of marbles

Total number of marbles \(n=6 + 3+1 = 10\)

Step2: Number of non - blue marbles

Number of non - blue marbles \(=6 + 1=7\)

Step3: Calculate probability

The probability \(P(\text{not blue})=\frac{\text{Number of non - blue marbles}}{\text{Total number of marbles}}=\frac{7}{10}\)

Answer:

C

Question 8