Question

HELP--30 POINTS

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.

1: 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

2: Explain the difference between the two probabilities you found in part 1.

3 What is the theoretical probability and likelihood of getting four black marbles in a row?

Answer 1

I just answerd this like 1 week ago


1.
theoretical is not counting the  results of the experiments
since 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 tests
4 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 so
1/(4*4)=1/16

Answer 2

Hello there

If inside the bag you have equal number of black, red and white, the theoretical probability of:

- Taking 1 black is 1/3.

Pt (b) = 1/3

- Taking one black and a second black again is

Pt (b&b) = 1/3 * 1/3 = 1/9

- Taking four blacks is

Pt (b & b & b & b) = $(1/3)^{4}$ = 1/81

When we talk about the experimental probability we refer to what had happened when we did it.

For calculating it we make the quotient between “observed frequency of the specific even” and “total number of trials”.

In this case Pe = 4/4 = 1

So

1) Pt (4b) = 1/81

Pe (4b) = 1

2) The explanation above.

3) the explanation above, too.

Kind regards,

Daniela