he owners of a two-person business make their decisions independently of each other and then compare their decisions. If they agree, the decision is made; if they do not agree, then further consideration is necessary before a decision is reached. Each has a history of making the right decision 55% of the time.
What is your question?
To analyze the decision-making process of the two-person business, we can use probability calculations.
Let's denote the probability of making the right decision by person A as PA and the probability of making the right decision by person B as PB. Given that each person has a history of making the right decision 55% of the time, we can express these probabilities as:
PA = 0.55
PB = 0.55
Now, let's consider the different scenarios that can occur when the two persons make independent decisions and compare them:
1. They both make the right decision:
Probability = PA * PB
2. They both make the wrong decision:
Probability = (1 - PA) * (1 - PB)
3. They have differing decisions:
Probability = 1 - (Probability of agreement)
The probability of agreement can be calculated by adding the probabilities of scenarios 1 and 2:
Probability of agreement = PA * PB + (1 - PA) * (1 - PB)
Let's calculate these probabilities:
Probability of agreement = 0.55 * 0.55 + (1 - 0.55) * (1 - 0.55)
= 0.3025 + 0.2025
= 0.505
Therefore, the probability of agreement is 0.505.
To find the probability of needing further consideration before a decision is reached, we subtract the probability of agreement from 1:
Probability of needing further consideration = 1 - Probability of agreement
= 1 - 0.505
= 0.495
Therefore, the probability of needing further consideration before a decision is reached is 0.495, or 49.5%.
To determine the probability of the owners making the right decision, we can use the principle of independent events.
Let's break down the decision-making process into two steps:
Step 1: Owners make independent decisions
Each owner has a 55% chance of making the right decision, which means there is a 45% chance of making the wrong decision. Since the owners make their decisions independently, the probability that they both make the right decision is 0.55 * 0.55 = 0.3025 (30.25%).
Step 2: Owners compare their decisions
If the owners both make the same decision, the decision is made. The probability of them agreeing is equal to the probability of both making the right decision, which is 0.3025 (30.25%).
However, if the owners do not agree, further consideration is necessary before a decision is reached. This means that the probability of disagreement is 1 - probability of agreement, which is 1 - 0.3025 = 0.6975 (69.75%).
So, in summary:
- The probability of the owners agreeing and making a decision is 0.3025 (30.25%).
- The probability of the owners disagreeing and requiring further consideration is 0.6975 (69.75%).