The roll of two dice - LA Mission

the roll of two dice activity

1. Suppose you roll two die: (a) What is the probability of rolling doubles (i.e. 2 and 2, or 3 and 3)? (b) What is the probability of rolling at least one 6? (c) What is the probability of not rolling doubles? (d) What is the probability of rolling a sum of 5? (e) What is the probability of not rolling a sum of 7?

2. Which of the following events are disjoint: (a) Rolling exactly one 6, and rolling exactly one 3 (b) Rolling doubles, and rolling at least one 4 (c) Rolling a sum of 8, and rolling at least one 1 (d) Rolling doubles, and rolling at least one 1 (e) Rolling doubles, and rolling exactly one 1

3. Change the `and' in exercise 2 to `or' now, and calculate the probabilities for each compound events. For example, for (a), calculate (Rolling exactly one 6 or rolling exactly one 3)

4. Find the following probabilities:

(a) (Rolling at least one 1 | Rolling at least one 3) (b) (Rolling doubles | Rolling a sum of 8) (c) (Rolling at least one 2 | Rolling a sum of 10) (d) (Rolling two 6s | Rolling at least one 6) (e) (Rolling two 6s | Rolling exactly one 6) (f) (Rolling two 6s | Rolling exactly two 6s)

5. Use the definition of independent events to determine which of these pairs of events are independent:

(a) Rolling doubles; rolling a sum of 8 (b) Rolling a sum of 8; getting a 2 on the first die rolled (c) Rolling a sum of 7; getting a 1 on the first die rolled (d) Rolling doubles; rolling a sum of 7 (e) Rolling a 1 on the first die; rolling a 1 on the second die

6. Use the multiplication, or the general multiplication rule to calculate the compound probabilities from exercise 5 by putting a "and" instead of the semicolon. For example, for (a), calculate (Rolling doubles and Rolling a sum of 8).

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