Question

NEED HELP ASAP! TYSM!
Erik is performing a marble experiment in math class. His teacher places an equal number of black, red, and white marbles in a bag. Then, Erik randomly takes out a marble, records the result, and puts the marble back in the bag. Each of the first four times Erik takes out a marble, he gets a black marble.
A. What is the theoretical probability of Erik picking a black marble next time? Based on Erik's results, what is the experimental probability of Erik picking a black marble next time?
B. Explain the difference between the two probabilities you found in part A.
C. What is the theoretical probability and likelihood of getting four black marbles in a row?
You have to answer each one! Thanks SO much! ^-^

Answer 1

1.theoretical is not counting the  results of the experimentssince there are an equal number of red and black and red, the probblity (theoretical) of picking a black one is 1/3
experimental=number of outcomes happened/total number of tests4 times black, 4 tests, so 4/4 or 100%=experimental proablity

2. experimental considered previous trials and theoretical did not

3.  theoretical=(1/4) the trials don't influence each other so1/(4*4)=1/16

Answer 2

A. The theoretical probability of an event can be obtained by comparing the number of desired outcomes to the number of possible outcomes.. In the case of equal amounts of marbles for 3 different colors in a bag, you would have a probability of $\frac{1}{3}$ for any one selection of a marble... Note, it is of interest that we replace the marble each time and thus maintain the equal likelihood of drawing a specified color with each new draw(previous draws have absolutely no impact on future draws).. Now, in the case of experimental probability we compare the number of desired outcomes to the number of trials In this case, Erick's results reveal drawing 4 black marbles in 4 trials, or a probability of 4 out of 4 or 100%. Based on this experimental probability you might be inclined to think you have 100% probability of drawing a black marble on the 5th draw..

B.. I've answered the difference between theoretical and experimental probability in part A

C. Each draw is an independent event. As such, to find the probability of these successive independent events all together we simply multiply the probability of each independent event together. $\frac{1}{3}( \frac{1}{3})( \frac{1}{3})(\frac{1}{3})= \frac{1}{81}$