(a) If you roll a single die and count the number of dots on top, what is the sa

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?

(b) Assign probabilities to the outcomes of the sample space of part (a). (Enter your answers as fractions.)

Do the probabilities add up to 1? Should they add up to 1? Explain.

(c) What is the probability of getting a number less than 5 on a single throw? (Enter your answer as a fraction.)
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(d) What is the probability of getting 4 or 5 on a single throw? (Enter your answer as a fraction.)
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Explanation / Answer

a) Yes, they are all equally likely - each face of the die has a 1/6 chance of being rolled.. so your sample space is 1-6 -- written {1, 2, 3, 4, 5, 6}..

b) Each face of the die has a 1/6 chance of being rolled:

Probability of rolling a 1: 1/6
Probability of rolling a 2: 1/6
Probability of rolling a 3: 1/6
Probability of rolling a 4: 1/6
Probability of rolling a 5: 1/6
Probability of rolling a 6: 1/6

Adding them up = 1. And yes, they should add up to one b/c that is justifying that every possibility was accounted for.

c) A number less than five - so our possibilities are 1, 2, 3, and 4.. As mentioned, each have a 1/6 chance of being rolled - in other words a probability of 4/6 = 2/3 or a 66.67% chance of rolling a 1, 2, 3, or 4...

d) Again, we have a 1/6 chance to roll a 4 or 5 -- in other words, a probability of 2/6 = 1/3 or a 33.33% chance of rolling a 5 or a 6..

**Notice how parts c and d add up to 1 or 100% as each possible outcome is accounted for..

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