Discussion Questions 1. Why are the “With Replacement” and “Without Replacement” probabilities different?

2. Convert P(no yellows) to decimal format for both Theoretical “With Replacement” and for Empirical “With

Replacement”. Round to four decimal places.

a. Theoretical “With Replacement”: P(no yellows) =

b. Empirical “With Replacement”: P(no yellows) =

c. Are the decimal values “close”? Did you expect them to be closer together or farther apart? Why?

3. If you increased the number of times you picked two M&Ms to 240 times, why would empirical probability

values change?

4. Would this change (see part 3) cause the empirical probabilities and theoretical probabilities to be closer together or farther apart? How do you know?

5. Explain the differences in what P(G1 AND R2) and P(R1|G2) represent. Hint: Think about the sample space for

each probability.

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°

75%

step-by-step explanation: