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Count out 40 mixed-color M&M’s® which is approximately 1 small bag’s worth (distance learning classes using the virtual lab would want to count out 25 M&M’s®). Record the number of each color in the "Population" table. Use the information from this table to complete the theoretical probability questions. Next, put the M&M’s in a cup. The experiment is to pick 2 M&M’s, one at a time. Do not look at them as you pick them. The first time through, replace the first M&M before picking the second one. Record the results in the “With Replacement” column of the empirical table. Do this 24 times. The second time through, after picking the first M&M, do not replace it before picking the second one. Then, pick the second one. Record the results in the “Without Replacement” column section of the "Empirical Results" table. After you record the pick, put both M&M’s back. Do this a total of 24 times, also. Use the data from the "Empirical Results" table to calculate the empirical probability questions. Leave your answers in unreduced fractional form. Do not multiply out any fractions.
Color | Quantity |
---|---|
Yellow (Y) | |
Green (G) | |
Blue (BL) | |
Brown (B) | |
Orange (O) | |
Red (R) |
With Replacement | Without Replacement | |
---|---|---|
$P\left(\text{2 reds}\right)$ | ||
$P\left({R}_{1}{B}_{2}\text{OR}{B}_{1}{R}_{2}\right)$ | ||
$P\left({R}_{1}\text{AND}{G}_{2}\right)$ | ||
$P\left({G}_{2}\text{|}{R}_{1}\right)$ | ||
$P\left(\text{no yellows}\right)$ | ||
$P\left(\text{doubles}\right)$ | ||
$P\left(\text{no doubles}\right)$ |
With Replacement | Without Replacement |
---|---|
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
( __ , __ ) ( __ , __ ) | ( __ , __ ) ( __ , __ ) |
With Replacement | Without Replacement | |
---|---|---|
$P\left(\text{2 reds}\right)$ | ||
$P\left({R}_{1}{B}_{2}\text{OR}{B}_{1}{R}_{2}\right)$ | ||
$P\left({R}_{1}\text{AND}{G}_{2}\right)$ | ||
$P\left({G}_{2}\text{|}{R}_{1}\right)$ | ||
$P\left(\text{no yellows}\right)$ | ||
$P\left(\text{doubles}\right)$ | ||
$P\left(\text{no doubles}\right)$ |
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