A single die is rolled.
(a) What is the probability that the number on top is a 3. (Give your answer correct to two decimal places.)
(b) What is the probability that the number on top is an odd number. (Give your answer correct to two decimal places.)
(c) What is the probability that the number on top is a number less than 5. (Give your answer correct to two decimal places.)
(d) What is the probability that the number on top is a number no greater than 3. (Give your answer correct to two decimal places.)
To solve these probability problems, we need to understand the total number of possible outcomes and the number of successful outcomes for each event.
In the case of rolling a single die, there are 6 possible outcomes (numbers 1, 2, 3, 4, 5, 6) and each outcome has an equal probability of 1/6.
Let's solve each question step by step:
(a) To find the probability of rolling a 3, we need to determine the number of successful outcomes (getting a 3) and divide it by the total number of possible outcomes. In this case, there is only one successful outcome (getting a 3), so the probability is 1/6.
(b) To find the probability of rolling an odd number, we need to determine the number of successful outcomes (getting a 1, 3, or 5) and divide it by the total number of possible outcomes. There are three successful outcomes (1, 3, and 5), so the probability is 3/6, which simplifies to 1/2.
(c) To find the probability of rolling a number less than 5, we need to determine the number of successful outcomes (getting a 1, 2, 3, or 4) and divide it by the total number of possible outcomes. There are four successful outcomes (1, 2, 3, and 4), so the probability is 4/6, which simplifies to 2/3.
(d) To find the probability of rolling a number no greater than 3, we need to determine the number of successful outcomes (getting a 1, 2, or 3) and divide it by the total number of possible outcomes. There are three successful outcomes (1, 2, and 3), so the probability is 3/6, which simplifies to 1/2.
Therefore, the answers are:
(a) The probability of rolling a 3 is 1/6.
(b) The probability of rolling an odd number is 1/2.
(c) The probability of rolling a number less than 5 is 2/3.
(d) The probability of rolling a number no greater than 3 is 1/2.