Question

Guilt in decision making. The effect of guilt emotion on how a decision maker focuses on the problem was investigated in the Jan. A total of 171 volunteer students participated in the experiment, where each was randomly assigned to one of three emotional states (guilt, anger, or neutral) through a reading/writing task. Immediately after the task, the students were presented with a decision problem where the stated option has predominantly negative features (e.g., spending money on repairing a very old car). The results (number responding in each category) are summarized in the accompanying table. Suppose one of the 171 participants is selected at random.
Emotional state choose stated option Do not choose staed option Totals
Guilt 45 12 57
Anger 8 50 58
Neutral 7 49 56
Totals 60 111 171
a. Find the probability that the respondent is assigned to the guilty state.
b. Find the probability that the respondent chooses the stated option (repair the car).
c. Find the probability that the respondent is assigned to the guilty state and chooses the stated option.
d. Find the probability that the respondent is assigned to the guilty state or chooses the stated option.

Answer 1

Answer:

a) 33.33% probability that the respondent is assigned to the guilty state.

b) 35.09% probability that the respondent chooses the stated option (repair the car).

c) 26.32%  probability that the respondent is assigned to the guilty state and chooses the stated option.

d) 40.94% probability that the respondent is assigned to the guilty state or chooses the stated option.

Step-by-step explanation:

A probability is given by the number of desired outcomes divided by the number of total outcomes. We use this concept, along with the given table, to solve the question.

a. Find the probability that the respondent is assigned to the guilty state.

There were 171 participants, and 57 of those were assigned the guilty state. So this probability is $p = \frac{57}{171} = 0.3333$

b. Find the probability that the respondent chooses the stated option (repair the car).

There were 171 participants, and 60 of those choose the stated option. So this probability is $p = \frac{60}{171} = 0.3509$

c. Find the probability that the respondent is assigned to the guilty state and chooses the stated option.

There were 171 participants, and 45 of those were assigned to the guilty state and choose the stated option. So this probability is $p = \frac{45}{171} = 0.2632$

d. Find the probability that the respondent is assigned to the guilty state or chooses the stated option.

Guilty state: 57

Anger or Neutral and stated option: 8 + 7 = 15

Total = 57 + 15 = 72

$p = \frac{70}{171} = 0.4094$