37% of all doctors are family practitioners. If four doctors are picked at
random, what is the probability that all four are family practitioners?
a.1.48
b.0.0187
c. 0.0168
d. .1369
To find the probability that all four doctors picked at random are family practitioners, we need to multiply the probability of picking a family practitioner for each doctor.
Given that 37% of all doctors are family practitioners, the probability of picking a family practitioner for the first doctor is 37% or 0.37.
Since each doctor is picked at random, the probability of picking a family practitioner for the second doctor is also 37% or 0.37.
Similarly, the probability of picking a family practitioner for the third doctor is 37% or 0.37.
And finally, the probability of picking a family practitioner for the fourth doctor is also 37% or 0.37.
To find the overall probability, we multiply these probabilities together:
0.37 * 0.37 * 0.37 * 0.37 = 0.037037
Therefore, the probability that all four doctors picked at random are family practitioners is approximately 0.037037.
Looking at the answer choices, we can see that option c. 0.0168 is the closest to this value.