andrea rolls a number cube twice. she determines p(even, then odd) = 1/2. which statements are accurate…

andrea rolls a number cube twice. she determines p(even, then odd) = 1/2. which statements are accurate? check all that apply. andreas solution is incorrect. the total number of possible outcomes is 12. the probability of each simple event is 1/2. there are three possible outcomes on each number cube. the probability of the compound event is less than the probability of either event occurring alone. p(even, then odd) = p(odd, then even)

andrea rolls a number cube twice. she determines p(even, then odd) = 1/2. which statements are accurate? check all that apply. andreas solution is incorrect. the total number of possible outcomes is 12. the probability of each simple event is 1/2. there are three possible outcomes on each number cube. the probability of the compound event is less than the probability of either event occurring alone. p(even, then odd) = p(odd, then even)

Answer

Explanation:

Step1: Calculate total outcomes

When rolling a number - cube twice, by the fundamental counting principle, the total number of possible outcomes is (6\times6 = 36), not 12.

Step2: Calculate probability of simple events

The probability of getting an even number ((2), (4), (6)) on a single roll of a number - cube is (P(\text{even})=\frac{3}{6}=\frac{1}{2}), and the probability of getting an odd number ((1), (3), (5)) on a single roll is (P(\text{odd})=\frac{3}{6}=\frac{1}{2}).

Step3: Calculate compound - event probability

Since the two rolls are independent events, (P(\text{even, then odd})=P(\text{even})\times P(\text{odd})=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\neq\frac{1}{2}), so Andrea's solution is incorrect. Also, (P(\text{odd, then even}) = P(\text{odd})\times P(\text{even})=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}), so (P(\text{even, then odd})=P(\text{odd, then even})). The probability of each simple event (even or odd on a single roll) is (\frac{1}{2}), and there are 6 possible outcomes on each number - cube. The probability of the compound event (P(\text{even, then odd})=\frac{1}{4}) which is less than the probability of either event occurring alone ((\frac{1}{2})).

Answer:

Andrea's solution is incorrect. The probability of each simple event is (\frac{1}{2}). The probability of the compound event is less than the probability of either event occurring alone. (P(\text{even, then odd}) = P(\text{odd, then even}))