You roll a pair of fair 6-sided dice: a red die and a blue die. (a)...

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You roll a pair of fair 6-sided dice: a red die and a blue die. (a)...

You roll a pair of fair 6-sided dice: a red die and a blue die.

(a) Consider event A: {the outcome of the red die is more than 3} and event B: {the outcome of the red die is less than 5}. Given that event A occurs, what is the probability that event B occurs?

(b) Are A and B mutually exclusive (i.e., disjoint)?

(c) Are A and B independent?

(d) Calculate the probability of event C: {the outcome of the red die is equal to the outcome of the blue die}.

(e) Consider event D: {the outcome of the red die is equal to 1}. Calculate the probability of event C given that event D occurs.

(f) Are C and D independent?

(g) Consider event E: {at least one die has an outcome equal to 2}. Calculate the probability of event E given that event D occurs.

math Statistics-And-Probability

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