Below are listed the numbers of doctors in various specialties by gender.
Pathology Pediatric Psychiatry
Male 12,575 33,020 27,803
Female 5,604 33,351 12,292
Choose 1 doctor at random.
(a) Find the probability of choosing a Pathologist or a female?
b.) Find the probability of choosing a male, given that they are pediatrician.
a. Pathologist = (12,575+5,604)/ grand total
Female = female total/grand total
Either-or probabilities are found by adding the individual probabilities.
b. 33,020/(33,020+33,351) = ?
ddedede
(a) To find the probability of choosing a Pathologist or a female, we need to add the probabilities of choosing a Pathologist and choosing a female and then subtract the probability of choosing both (as it would have been counted twice).
Let's find the probability of choosing a Pathologist first:
Total doctors in Pathology = Male Pathologists + Female Pathologists = 12,575 + 5,604 = 18,179
Total doctors in all specialties = Sum of all male doctors + Sum of all female doctors = 12,575 + 5,604 + 33,020 + 33,351 + 27,803 + 12,292 = 124,645
Probability of choosing a Pathologist = Total doctors in Pathology / Total doctors in all specialties = 18,179 / 124,645 ≈ 0.1459
Now let's find the probability of choosing a female:
Total female doctors in all specialties = Sum of all female doctors = 5,604 + 33,351 + 12,292 = 51,247
Probability of choosing a female = Total female doctors / Total doctors in all specialties = 51,247 / 124,645 ≈ 0.4109
Next, let's find the probability of choosing both a Pathologist and a female:
Probability of choosing a Pathologist and a female = Probability of choosing a Pathologist * Probability of choosing a female = 0.1459 * 0.4109 ≈ 0.0599
Finally, let's calculate the probability of choosing a Pathologist or a female:
Probability of choosing a Pathologist or a female = Probability of choosing a Pathologist + Probability of choosing a female - Probability of choosing both = 0.1459 + 0.4109 - 0.0599 ≈ 0.497≈49.7%
Therefore, the probability of choosing a Pathologist or a female is approximately 49.7%.
(b) To find the probability of choosing a male, given that they are a pediatrician, we need to calculate the conditional probability.
Total male doctors in Pediatrics = 33,020
Total doctors in Pediatrics = 33,020 + 33,351 = 66,371
Probability of choosing a male given that they are a pediatrician = Total male doctors in Pediatrics / Total doctors in Pediatrics = 33,020 / 66,371 ≈ 0.4977 ≈ 49.8%
Therefore, the probability of choosing a male, given that they are a pediatrician, is approximately 49.8%.
To find the probabilities in each scenario, we will need to use the total number of doctors in each specialty as well as the total number of doctors overall.
Given data:
Pathology - Male: 12,575, Female: 5,604
Pediatric - Male: 33,020, Female: 33,351
Psychiatry - Male: 27,803, Female: 12,292
Total doctors in each specialty:
Pathology: 12,575 + 5,604 = 18,179
Pediatric: 33,020 + 33,351 = 66,371
Psychiatry: 27,803 + 12,292 = 40,095
Total doctors overall: 18,179 + 66,371 + 40,095 = 124,645
(a) Probability of choosing a Pathologist or a female:
To calculate this probability, we need to add the number of doctors in each specialty/ gender category (Pathologist male + Pathologist female) and divide it by the total number of doctors overall.
Total Pathologists: 12,575 + 5,604 = 18,179
Total females: 5,604 + 33,351 + 12,292 = 51,247
P(Pathologist or female) = (18,179 + 51,247) / 124,645
(b) Probability of choosing a male, given that they are a pediatrician:
To calculate this probability, we need to determine the number of male pediatricians and divide it by the total number of pediatricians.
P(Male | Pediatrician) = Male Pediatricians / Total Pediatricians
P(Male | Pediatrician) = 33,020 / (33,020 + 33,351)