Question

3. Describe the similarities and differences among the following experiments. (a) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, two slips are drawn simultaneously. (b) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, one slip is drawn then put back into the box, then a second slip is drawn. (c) Slips of paper are marked with the numbers 1, 2, 3, 4, and 5 and placed into a box. After being mixed, one slip is drawn and not put back into the box, then a second slip is drawn.

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Describe the first experiment

Two slips were drawn simultaneously, this means that the outcome of the first slip drawn will be multiplied by the outcome of the second slip drawn. The probability will follow the "and rule of probability".

STEP 2: Describe the second experiment

Since one slip is drawn and then put back into the box before a second slip is drawn, this is a PROBABILITY WITH REPLACEMENT. The outcome of the first event will not affect the outcome of the second event since the paper slips are replaced hence not reduced.

STEP 3: Describe the third experiment

Since one slip is drawn and not put back into the box before a second slip is drawn, this is a PROBABILITY WITHOUT REPLACEMENT. The outcome of the first event will affect the outcome of the second event since the paper slips reduce.

Difference between b and c is that b is with replacement and the total outcomes does not change while c is without replacement and the total outcomes change(reduce) after the first slip is drawn.