M & Ms Instructions. Use the following abbreviations: r = red, g = green, bl = blue, o = orange, b = brown, y = yellow. There is a video in Resources.
With Replacement Table: After the first M & M is selected, click the first box of the ordered pair (you will NOT see a cursor in the box) and type the abbreviation for that color. Then select the second M & M, click the second box of the ordered pair and type the abbreviation for that color. Do this procedure for the 24 pairs.
Without Replacement Table: After both M & Ms are selected, click the first box of the ordered pair, enter the abbreviation, click the second box of the ordered pair, and enter that abbreviation. Do this procedure for the 24 pairs.
After you have taken data for "With Replacement" and "Without Replacement", make sure you print the page with the data and include it when you hand the lab in.
Example: You are working with 25 M & Ms. Fill out the theoretical chart. Use the data you took online for your empirical charts.
THEORETICAL probabilities use the theoretical chart. Suppose I have 5Y (yellow), 4G (green), 2Bl (blue), 6B (brown), 5O (orange),and 3R (red) [Total: 25 M & Ms}.
With replacement: You draw the first M & M, put it back, and draw the 2nd. For each draw you have a total of 25 M & Ms to draw from.
P(2 reds) = P(R and R) = (3/25)for the first draw multiplied by (3/25) for the second draw = (3/25)(3/25). You can leave the answer in this form. You will understand it better.
NOTE: R1 means red on the first draw. B2 means brown on the 2nd draw, etc.
P(R1B2 or B1R2) = P(R1 and B2) + P(B1 and R2)= (3/25)(6/25) + (6/25)(3/25)
P(R1 and G2) = (3/25)(4/25)
P(G2|R1) = P(R1 and G2)/P(R1) = (3/25)(4/25)/3/25) = 4/25
P(no yellows) means on either draw, you do not draw a yellow. There are 20 no yellows. P(no yellows)= (20/25)(20/25)
P(doubles) = P(R and R) + P(G and G) + P(Bl and Bl) + P(B and B) + P(O and O) + P(Y and Y)
Doubles and no doubles are complements so P(doubles)+P(no doubles) = 1
Without replacement: You draw the first M & M, KEEP IT OUT,and draw the 2nd. Then put BOTH M & Ms back to draw the next pair. For the first draw you have a total of 25 M & Ms and the second draw, 24 M & Ms.
P(2 reds) = P(R and R) = (3/25) for the first draw multiplied by (2/24) for the second draw = (3/25)(2/24). You can leave the answer in this form. You will understand it better.
NOTE: R1 means red on the first draw. B2 means brown on the 2nd draw, etc.
P(R1B2 or B1R2) = P(R1 and B2) + P(B1 and R2) = (3/25)(6/24) + (6/25)(3/24)
P(R1 and G2) = (3/25)(4/24)
P(G2|R1) = P(R1 and G2)/P(R1) = (3/25)(4/24)/3/25) = 4/24
P(no yellows) means on either draw, you do not draw a yellow. There are 20 no yellows. P(no yellows)= (20/25)(19/24)
P(doubles) = P(R and R) + P(G and G) + P(Bl and Bl) + P(B and B) + P(O and O) + P(Y and Y)
Doubles and no doubles are complements so P(doubles)+P(no doubles) = 1
For the EMPIRICAL probabilities for both with and without replacement, just count the ordered pairs in the chart and divide by 24. The exception is P(G2|R1). Leave your answers as fractions.
P(2 reds) = P(R and R)= all ordered pairs that are (R,R) divided by 24 ordered pairs. So, if there are 7 ordered pairs that are (R,R), the probability is 7/24.
P(G2|R1) = all ordered pairs (R,G) out of the order pairs that are (R,anything). For example, suppose the (R,anything) ordered paires are (R,G), (R,G), (R,Y), (R,B), (R,B), (R,Bl). There are 6 of these ordered pairs and 2 of them are (R,G) so the probability is 2/6.
Make sure you answer the all questions in the lab. MAKE SURE YOU ATTACH YOUR DATA PAGE.
