Question

O DATA ANALYSIS AND STATISTICS Outcomes and event probability A number cube is rolled three times. An outcome is represented by a string of the sort OEE (meaning an odd number on the first roll, an even number on the second roll, and an even number on the third roll). The S outcomes are listed in the table below. Note that each outcome has the same probability. For each of the three events in the table, check the outcome(s) that are contained in the event. Then, in the last column, enter the probability of the event. Event A: No even numbers on the last two rolls Event B: An even number on the last roll or the second roll (or both) Event C: An even number on both the first and the last rolls Explanation Check JU EOO 000 OOE O Outcomes EEO EOE OEE EEE 0 0 H 0 OEO Probability O 0 0 00 믐 15 X ? C2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Center Nikida Español K Accessibility

Answer 1

ANSWER

EXPLANATION

For each of the three events, there are 8 possible outcomes, so the probability of each event is,

$P(event)=\frac{favorable\text{ }outcomes}{possible\text{ }outcomes}=\frac{favorable\text{ }outcomes}{8}$

• Event A:, there must be only odd numbers in the last two rolls, which are either ,EOO or OOO,. This event has 2 favorable outcomes, ,so its probability is 1/4,.

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• Event B,: this is the complementary event to event A. Here the last two rolls must be even numbers - both or only one of the last two: ,OOE, EEO, EOE, OEE, EEE, OEO,. This event has 6 favorable outcomes, so ,its probability is 3/4,.

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• Event C,: this event is when the first and last rolls are even numbers in the same event. This is either ,EOE or EEE,. Since this event has 2 favorable outcomes, ,its probability is 1/4,.