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Question 1

A)There are two events, A and B. How do you mathematically determine whether events A and B are independent?(1 point)
Responses

P(A and B)=P(A)⋅P(B)
upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis times upper P left parenthesis upper B right parenthesis

P(A and B)=P(A)−P(B)
upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis minus upper P left parenthesis upper B right parenthesis

P(A and B)=P(A)+P(B)
upper P left parenthesis upper A and upper B right parenthesis equals upper P left parenthesis upper A right parenthesis plus upper P left parenthesis upper B right parenthesis

P(A and B)=P(A)P(B)
upper P left parenthesis upper A and upper B right parenthesis equals Start Fraction upper P left parenthesis upper A right parenthesis over upper P left parenthesis upper B right parenthesis End Fraction
Question 2
A)There are 16 marbles in a jar: 5 red, 3 blue, and 8 yellow. What is the probability of selecting a blue marble and then, without replacing the blue marble, selecting a yellow marble?(1 point)
Responses

332
Start Fraction 3 over 32 End Fraction

110
Start Fraction 1 over 10 End Fraction

1116
Start Fraction 11 over 16 End Fraction

173240
Start Fraction 173 over 240 End Fraction
Question 3
A)
Use the table to answer the question.

Arrival Time
Transport Type On Time Late TOTAL
Car 164 48 212
Bus 46 62 108
TOTAL 210 110 320
Let event A represent an on-time arrival and event B represent transportation by bus. What is P(A and B)? Round your answer to the nearest hundredth.

(1 point)
Responses

0.34
0.34

0.14
0.14

0.22
0.22

0.43
0.43
Question 4
A)Which of the following explains the concept of independence in everyday life experiences?(1 point)
Responses

selecting a fruit from a basket and keeping each fruit until you get the fruit that you want
selecting a fruit from a basket and keeping each fruit until you get the fruit that you want

randomly pulling out 1 fruit at a time and setting them aside until you get the color that you want
randomly pulling out 1 fruit at a time and setting them aside until you get the color that you want

selecting a fruit from a basket without looking and replacing it until you get your desired fruit
selecting a fruit from a basket without looking and replacing it until you get your desired fruit

8 people randomly selecting from 8 fruits and keeping what they chose
8 people randomly selecting from 8 fruits and keeping what they chose
Question 5
A)A regular six-sided number cube is being used to determine the number of spaces a player is allowed to move in a game. What is the sample space of this number cube?(1 point)
Responses

2, 4, 6
2, 4, 6

1, 2, 3, 4, 5, 6
1, 2, 3, 4, 5, 6

1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6

1 answer

Here are the answers to your questions:

Question 1: A) The correct mathematical condition for determining whether events A and B are independent is:

  • P(A and B) = P(A) ⋅ P(B)

Question 2: A) To find the probability of selecting a blue marble followed by a yellow marble without replacement, you calculate:

  • The probability of selecting a blue marble: \( \frac{3}{16} \)
  • The probability of selecting a yellow marble after selecting a blue marble: \( \frac{8}{15} \)
  • Thus, \( P(\text{blue followed by yellow}) = \frac{3}{16} \times \frac{8}{15} = \frac{24}{240} = \frac{1}{10} \)
  • The correct answer is:
  • Start Fraction 1 over 10 End Fraction

Question 3: A) To find \( P(A \text{ and } B) \) (the probability of an on-time arrival via bus):

  • Total on-time arrivals (A): 210
  • On-time arrivals by bus (A and B): 46
  • Therefore, \( P(A \text{ and } B) = \frac{46}{320} = 0.14375 \) which rounds to 0.14
  • The correct answer is:
  • 0.14

Question 4: A) The expression that best explains the concept of independence in everyday life is:

  • selecting a fruit from a basket without looking and replacing it until you get your desired fruit
  • This implies that the selection process does not affect the subsequent selections.

Question 5: A) The sample space for a regular six-sided number cube (die) is:

  • 1, 2, 3, 4, 5, 6

Overall summarized answers:

  1. P(A and B) = P(A) ⋅ P(B)
  2. Start Fraction 1 over 10 End Fraction
  3. 0.14
  4. selecting a fruit from a basket without looking and replacing it until you get your desired fruit
  5. 1, 2, 3, 4, 5, 6