Respuesta :
Answer:
The probability that you take exactly 15 calls to reach your goal is 0.1240.
Step-by-step explanation:
Let X = number of calls that result in receiving $10.
The probability that a call result in receiving $10 is, p = 0.60.
The number of calls made to reach a goal of $100 is, n = 15.
The random variable X follows a Binomial distribution with parameters n = 15 and p = 0.60.
The probability mass function of X is:
[tex]P(X=x)={n\choose x}p^{x}(1-p)^{n-x};\ x=0,1,2,3...[/tex]
Now it is provided that it takes 15 calls to reach the goal, i.e. the 15th call was a success.
This implies that the probability of reaching the goal by the 15th call is same as the probability of 9 success in the previous 14 calls.
Compute the probability of 9 success in 14 calls as follows:
[tex]P(X=9)={14\choose 9}0.60^{9}(1-0.60)^{14-9}\\=2002\times 0.0101\times 0.01024\\=0.2066[/tex]
The probability of success in the 15th call is, 0.60.
Then the probability of reaching the goal by the 15th call
= P (X = 9) × 0.60
= 0.2066 × 0.60
=0.1240
Thus, the probability that you take exactly 15 calls to reach your goal is 0.1240.
