Question

Geoffrey and Sara are playing a game. They fill a bucket with 12 red marbles, 8 blue marbles and 4 green marbles. They are going to pull out a marble at random. They played the game 10 times and here are the results: green, green, blue, red, red, red, green, red, green, red. Are the empirical and theoretical probabilities the same? If so, why, if not, why not. Does your answer make sense?

Answer 1

Solution:-) P(R) - Probability of drawing Red marbles.

P(B) - Probability of drawing Blue marbles.

P(G) - Probability of drawing Green marbles.

The theoretical results by axioms of probability ;-

The empirical result will be , probability is calculated as p = no.of events occur/total no. of events

green, green, blue, red, red, red, green, red, green, red.

n(g) = 4 , n(b)=1 , n(r) =5

We, can see the approx results are the same for theoretical and empirical, but as the no. of events increase we will get more precise results.

CHEERS!!