Question

Question 7.

One of the crane drivers, Trevor, has a daughter who slips a small chocolate in her father’s lunch on 55% of working days. Trevor likes to share these with his two co-drivers, so waits until he has a collection of three chocolates before sharing and eating them.

(a) What probability model (with parameter value/s) is appropriate for the count of the number of days until the chocolates are eaten (from the previous time)?

(b) For the count of the number of lunches until the chocolates get shared and eaten:

(i) What is the expected number and standard deviation?

(ii) What is the probability that exactly five lunches are needed?

(c) Constructions cranes in general lift a total of 2,220,000 items during their working lifetimes.

The probability of dropping a load is 1 in 12 million.

What is the probability that more than one load is dropped over the working life of a crane?

Answer 1

a) Negative Binomial probability model will be appropriate to model the count of the no. of days until the chocolates are eaten.

p = 0.55, x = 3 successes, n trials

b) (i) Expected number = x/p = 3/0.55 = 5.45

Standard deviation = x (1-p)/p^2

x = 3 (0.45)/0.55^2

x = 4.46

(ii) P(n=5) = 4C2 . (0.55)^3 (0.45)^2

Probability = 0.20

c) Here, binomial distribution will be used.

n = 2,220,000

p = 1/12000000

We will find the probability = 1 - P(x=0) - p(x=1)

P = 1 - nCo.(1-p)^n - nC1.p.(1-p)^(n-1)

P = 1 - 0.831 - 0.154

P = 0.015