a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?1, 2, 3, 4, 5, 6; not equally likely0, 1, 2, 3, 4, 5, 6; not equally likely 1, 2, 3, 4, 5, 6; equally likely0, 1, 2, 3, 4, 5, 6; equally likely(b) Assign probabilities to the outcomes of the sample space of part (a). (Enter your answers as fractions.)Outcome Probability1 2 3 4 5 6 Do the probabilities add up to 1? Should they add up to 1? Explain.Yes, but they should not because these values do not cover the entire sample space.Yes, because these values cover the entire sample space. No, because these values do not cover the entire sample space.No, but they should because these values cover the entire sample space.(c) What is the probability of getting a number less than 2 on a single throw? (Enter your answer as a fraction.)(d) What is the probability of getting 1 or 2 on a single throw? (Enter your answer as a fraction.)
Question
a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?1, 2, 3, 4, 5, 6; not equally likely0, 1, 2, 3, 4, 5, 6; not equally likely 1, 2, 3, 4, 5, 6; equally likely0, 1, 2, 3, 4, 5, 6; equally likely(b) Assign probabilities to the outcomes of the sample space of part (a). (Enter your answers as fractions.)Outcome Probability1 2 3 4 5 6 Do the probabilities add up to 1? Should they add up to 1? Explain.Yes, but they should not because these values do not cover the entire sample space.Yes, because these values cover the entire sample space. No, because these values do not cover the entire sample space.No, but they should because these values cover the entire sample space.(c) What is the probability of getting a number less than 2 on a single throw? (Enter your answer as a fraction.)(d) What is the probability of getting 1 or 2 on a single throw? (Enter your answer as a fraction.)
Solution
a) The sample space of all possible outcomes when you roll a single die and count the number of dots on top is {1, 2, 3, 4, 5, 6}. Yes, the outcomes are equally likely because a fair die has an equal chance of landing on any of its six faces.
b) The probabilities of the outcomes are as follows:
Outcome Probability 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6
Yes, the probabilities add up to 1. They should add up to 1 because the probabilities of all possible outcomes of a random experiment should always add up to 1. This is a fundamental principle of probability.
c) The probability of getting a number less than 2 on a single throw is 1/6 because the only number less than 2 on a die is 1.
d) The probability of getting 1 or 2 on a single throw is 1/6 + 1/6 = 2/6 = 1/3 because there are two favorable outcomes (1 and 2) and six possible outcomes in total.
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