A college student is employed as a door-to-door newspaper salesman. Historical d

Question

A college student is employed as a door-to-door newspaper salesman. Historical data suggests that the student sells a subscription to 6% of the homes he visits. Suppose the student begins going door-to-door at some point in time.

- Given that 2 subscriptions are sold at the first 24 homes, what is the probability that the 4th subscription is sold at the 36th home?

- What is the probability that exactly 4 subscriptions are sold at the first 51 homes?

- What is the probability that no more than 2 subscriptions are sold at the first 18 homes?

Explanation / Answer

p = 0.06

#1.
Out of 36 subscriptions, 2 are sold at first 24 homes.
Now out of 12 one is sold at last
Hence we need to determine 1 subscription sold in remaining 11 visits

Hence required probabiltiy is 11C1*(0.06)*(0.94)^10 * 0.06 = 0.02133

#2.
Probability that exactly 4 subscriptions sold = 51C4 * 0.06^4 * 0.94^47 = 0.1768

#3.
Probability that no more than 2 subscriptions are sold =
18C0 * 0.06^0 * 0.94^18
+ 18C1 * 0.06^1 * 0.94^17
+ 18C1 * 0.06^2 * 0.94^16

= 0.9102

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