Question

In a scavenger hunt, only 25% of people found a golden egg. Would it be usual for 6 people to find an egg when there are 20 people looking for eggs? Explain the answer with specific detail as to why or why not.

Answer 1

Let X be the number of people who find the golden egg

As finding the golden egg is independent for each person and probability is constant ( 0.25) for each person

X follow Binomial distribution with n= 20 , p=0.25

Probability mass function of a Binomial distribution  is

, x=0,1,2,...n

Here n= 20 , p=0.20

, x=0,1,2,....20

Thus , we get the probability that out of 20 , 6 people get golden egg is =0.1686

We know that if the probability of an event is less than 0.05 , then the event is considered unusual

As the calculated probability is much higher than 0.05 , the event of 6 people getting golden egg is not unusual.

Yes, it would be usual for six people to find an egg .