Question

Alan works as a cashier at a general store. He has a 9% chance of pulling out a 2004 quarter from his drawer.

He wants to know the probability that it takes at least four attempts to pull out a 2004 quarter.




Which simulation can best be used to compute the probability?

Answer 1

Model B: Draw a ball from a bag containing different balls numbered from 1 to 11. For one trial, draw a ball, with replacement, until the number 5 ball is drawn. Count the trial if the number 5 ball is drawn on the fourth draw or later. Repeat the process for 100 trials.

Explanation:

Answer 2

1. The probability that it takes at least four attempts to pull out a 2004 quarter is 0.0678

2. The best simulation to be used is the geometric distribution

Explanation:

Here, we have make use of the geometric probability distribution which allows us to find the number of Bernoulli trials are required to get a success or the probability that the first success of Bernoulli distribution, requires k trials

The relation for the geometric distribution is given as follows

`Pr (X = k) = (1-p)^(k-1)\cdot p`

Where:

X = Number of trial before success

k = The number of trials = 4

p = Probability of success = 9% = 0.09

Plugging in the values, we have;

Pr(4) = (1 - 0.09)⁴⁻¹×0.09 = 0.0678.