Question

a) At a carnival, the chance of winning the ring toss game is 10%. Show the probability distribution (table) for 5 games played.

b) If the carnival owner thinks that the average player has a 5% chance of winning the ring toss game, and about 500 people play each day, how many prizes should they keep in stock so that the probability of running out of prizes is less than 15% (using normal approximation)?

Answer 1

Answer:

Given that:

a) At a carnival, the chance of winning the ring toss game is 10%. Show the probability distribution (table) for 5 games played.

Chance of winning ring toss is 10%. Total number of games played is 5.

Let X be the variable representing number of games won among those 5.

So here X can take any value from 0, 1, 2, 3, 4 and 5.

Here X will follow Binomial Distribution with parameters n=5 and p=0.1

So probability distribution of X is given below.

b) If the carnival owner thinks that the average player has a 5% chance of winning the ring toss game, and about 500 people play each day, how many prizes should they keep in stock so that the probability of running out of prizes is less than 15%

500 people play per day and average player has a 5% chance of winning.

Let X be the variable representing the number of people winning the game.

So X will follow Binomial Distribution with parameter n=500 and p=0.5

So probability distribution of X is given below.

Let number of prize kept is k.

Then running out of prize will occur for X > k .

So the probability of running out of prizes is

As per condition this probability will be less than 0.15

From the cumulative distribution of binomial distribution we get

So value of k=30

So at least 30 prizes should be kept in stock so the probability of running out of prizes is less than 15%.