Question

If you roll a fair die and count the number of dots on top, a) What is the probability of rolling a number less than 4 on a single throw? b) What is the probability of rolling 2 or 5 on a single throw?

Answer 1

In a roll of a fair six-sided die, the probability of rolling a number less than 4 is 0.5, and the probability of rolling a 2 or 5 is approximately 0.3333.

Step-by-step explanation:

When rolling a fair six-sided die, the sample space S is {1, 2, 3, 4, 5, 6}, representing each possible outcome that can occur.

a) The probability of rolling a number less than 4 is simply the number of favorable outcomes (rolling a 1, 2, or 3) divided by the number of total outcomes in the sample space. There are 3 favorable outcomes and 6 possible outcomes, so the probability P(less than 4) = 3/6 = 0.5 or 50%.

b) To find the probability of rolling either a 2 or a 5, count the number of favorable outcomes for this event (2 and 5) and divide by the total number of outcomes. There are 2 favorable outcomes, so the probability P(rolling a 2 or 5) = 2/6 = 1/3, which is approximately 0.3333 or 33.33%.

Always round relative frequency and probability problems to four decimal places when asked to provide numerical answers.