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). 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? (d) What is the probability of getting 5 or 6 on a single throw?

Answer 1

SOLUTION:

From given data,

(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?

Sample space, S = {1, 2, 3, 4, 5, 6}

Yes, all outcomes are equally likely.

(b) Assign probabilities to the outcomes of the sample space of part (a). Do the probabilities add up to 1? Should they add up to 1? Explain.

The probabilities of each outcome are as given below

P(1) = 1/6

P(2) = 1/6

P(3) = 1/6

P(4) = 1/6

P(5) = 1/6

P(6) = 1/6

Sum of probabilities = 1/6 + 1/6 +1/6 + 1/6 + 1/6 + 1/6 = 1

The sum should add up to 1. This is because, the sum of all events in a sample space is always 1. This is one of the general condition to be met by a probability distribution.

(c) What is the probability of getting a number less than 5 on a single throw?

P(getting a number less than 5 on a single throw) = P(1) + P(2) + P(3) + P(4)

= 1/6 + 1/6 + 1/6+ 1/6

= 2/3

P(getting a number less than 5 on a single throw) = 2/3

(d) What is the probability of getting 5 or 6 on a single throw?

P(getting 5 or 6 on a single throw) = 1 - P(getting a number less than 5 on a single throw)

= 1 - 2/3

= 1/3

P(getting 5 or 6 on a single throw)= 1/3​​​​​​​