Respuesta :
Answer:
0.082
Step-by-step explanation:
Total number of clients = 4
From past experience, the agent knows that the probability of making a sale on any appointment is one out of five = 1/5.
This shows that there are only two possible outcomes, success or failure. It is either she makes a sale on an appointment or she fails to make a sale on the appointment. Therefore, we can use binomial distribution.
For binomial distribution,
P(x=r) = nCr × q^(n-r) × p^r
p = probability of making a sale on any appointment = 1/5 = 0.2
q = probability of not making a sale on any appointment = 1 -1/5 = 0.8
n = 5
x = 3
P(x=3) = 5C3 × 0.8^2 × 0.2^3
= 10×0.6724× 0.012167 =0.082
Answer:
2.56% probability that the agent will sell a policy to three of the four prospective clients
Step-by-step explanation:
For each client, there are only two possible outcomes. Either a policy is sold, or it is not. The probability of a policy being sold to a client is independent of other clients. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
An insurance agent has appointments with four prospective clients tomorrow.
This means that [tex]n = 4[/tex]
From past experience the agent knows that the probability of making a sale on any appointment is one out of five.
This means that [tex]p = \frac{1}{5} = 0.2[/tex]
Using the rules of probability, what is the likelihood that the agent will sell a policy to three of the four prospective clients?
This is P(X = 3).
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 3) = C_{4,3}.(0.2)^{3}.(0.8)^{1} = 0.0256[/tex]
2.56% probability that the agent will sell a policy to three of the four prospective clients
