It a salesperson is chosen at random the probability that his potential for advancement is Good given that his Sales Ability is Above Average is
The probability that the potential for advancement is Good given that the sales ability is Above Average can be denoted as P(Good | Above Average).
To calculate this probability, we need to know the probabilities of having Above Average Sales Ability (denoted as P(Above Average)) and the probability of having Good potential for advancement given Above Average Sales Ability (denoted as P(Good ∩ Above Average)).
Let's assume that P(Above Average) is 0.25 (25%) and P(Good ∩ Above Average) is 0.15 (15%).
P(Good | Above Average) can be calculated using the formula for conditional probability:
P(Good | Above Average) = P(Good ∩ Above Average) / P(Above Average)
So, plugging in the given values:
P(Good | Above Average) = 0.15 / 0.25
P(Good | Above Average) = 0.6
Therefore, the probability that the potential for advancement is Good given that sales ability is Above Average is 0.6 or 60%.
To calculate the probability that a salesperson's potential for advancement is Good given that their Sales Ability is Above Average, we need more information. Specifically, we need to know the conditional probabilities associated with the salespeople's potential for advancement and their sales ability.
If we have this information, we can use Bayes' theorem to calculate the probability. Bayes' theorem states that:
P(A|B) = (P(B|A) * P(A)) / P(B)
Where:
P(A|B) is the probability of event A given event B.
P(B|A) is the probability of event B given event A.
P(A) is the probability of event A.
P(B) is the probability of event B.
In our case:
Event A: Potential for Advancement is Good
Event B: Sales Ability is Above Average
If we have the conditional probabilities P(A|B) and P(B|A), we can use these values to calculate the probability we're looking for.