2) In a certain instant lottery game, the chances of a win stated as "3 in 23". Express the indicated degree of likelihood as a probability value between 0 and 1
3) A certain company reduced its management staff from 20 managers to 16. The company claimed that 4 managers were randomly selected for job termination. However, the four managers chosen are the four oldest managers among the 20 the were employed. Answer the questions below.
Part A: Find the probability that when the four managers are randomly selected from a group of 20, the four oldest are selected. The probability is.
Part B: Is that probability low enough to charge that instead of using random selection , the company actually fired the oldest employees.
A)No, because it would not be unusual to fire the oldest managers, given that they were randomly selected for termination
B)Yes, because it would be unusual to fire the oldest employees, if they were randomly selected for termination.
c) No, the probability is not low. Each manager had an equal chance of being fired.
D) Yes, the probability is low enough, therefore , it is possible that the oldest employees were randomly selected.
4) A research center poll showed that 83% of the people believe that it is morally wrong to not report all income on tax returns. What is the Probability that someone does not have this belief.
number of all possible groups of 4 is
C(20,4) = 4845
the group of 4 oldest is one of those
prob that the four oldest were picked randomly = 1/4845
I will leave the interpretations etc up to you
2) The indicated degree of likelihood can be expressed as a probability value between 0 and 1 by dividing the number of desired outcomes (in this case, a win) by the total number of possible outcomes (in this case, 23). So, the probability of winning the instant lottery game can be calculated as:
Probability of winning = Number of desired outcomes / Total number of possible outcomes
In this case, the number of desired outcomes is 3 (according to the statement "3 in 23") and the total number of possible outcomes is 23. Therefore, the probability of winning is:
Probability of winning = 3/23 ≈ 0.1304
So, the probability of winning the instant lottery game is approximately 0.1304.
3) Part A: To find the probability that the four oldest managers are selected when randomly selecting four managers from a group of 20, we need to determine the number of ways the four oldest managers can be selected divided by the total number of possible selections.
There are 20 managers in total, so the number of ways to select four managers from this group is given by the combination formula, which can be written as:
C(20, 4) = 20! / (4! * (20 - 4)!) = 4845
Out of these 4845 possible selections, only 1 selection would include the four oldest managers. Therefore, the probability that the four oldest managers are selected is:
Probability = 1 / 4845 ≈ 0.000206
So, the probability is approximately 0.000206.
Part B: The answer would be A) No, because it would not be unusual to fire the oldest managers, given that they were randomly selected for termination.
2) To express the indicated degree of likelihood as a probability value between 0 and 1, divide the number of favorable outcomes (in this case, the number of wins) by the total number of possible outcomes. In this scenario, the probability would be 3/23.
3)
Part A: To find the probability that the four oldest managers are selected when four managers are randomly chosen from a group of 20, we need to consider the number of ways the selection can occur. Since we are interested in the specific outcome where the four oldest managers are chosen, there is only 1 favorable outcome. The total number of possible outcomes is determined by the number of ways to select four managers out of the 20 available, which can be calculated using the combination formula. The probability would be 1 divided by the total number of possible outcomes.
Part B: The answer would be A) No, because it would not be unusual to fire the oldest managers, given that they were randomly selected for termination. The probability of firing the four oldest managers is dependent on the specific age distribution among the 20 managers. If the oldest managers happened to be clustered in a particular age range within the 20 managers, then it would not be unusual to see them being terminated.
4) To find the probability that someone does not have the belief that it is morally wrong to not report all income on tax returns, subtract the percentage of people who hold that belief (in this case, 83%) from 100% (the total probability). Therefore, the probability would be 100% - 83% = 17%.