Question

N a game show, a contestant randomly draws a chip from a bag and replaces it. The theoretical probability of drawing a winning chip is 3/10​​ . The bag contains 9 winning chips Out of 20 contestants, how many do you expect to draw a winning chip?

Answer 1

Answer:

I would expect 6 contestants to draw a winning chip each.

Step-by-step explanation:

Theoretical probability is basically = Number of successful outcomes/Number of possible outcomes.

Since the theoretical probability of drawing a winning chip is 3(winning chips)/10(total chips), if there are 9 winning chips in the bag, we need to first calculate the total number of chips in the bag using the principle of proportion.

Let's call the total number of chips in the bag, "x".

3/10 = 9/x

Cross multiplying:

3x = 90

x = 90/3

x = 30 chips

There is a total of 30 chips in the bag.

Now, if there are 9 winning chips in a bag that contains 30 chips altogether and 30 contestants are to draw one chip each from the bag, I would expect 9 contestants out of the 30 contestants that drew chips from the bag to draw winning chips.

Then if each of the 20 contestants are to draw a single chip from the bag of 30 chips, then the number of contestants that I would expect to draw a winning chip is:

30 contestants----------9 winning chips

20 contestants----------- ? winning chips

20/30 × 9

= 180/30

= 6 winning chips to be drawn by 6 different contestants.

Therefore the number of contestants that I would expect to draw a winning chip from the bag is 6