In Exercises 45-46, it is equally probable that the pointer on the spinner shown will land on any one of the eight regions, numbered 1 through 8. If the pointer lands on a borderline, spin again. Find the probability that the pointer will stop on an odd number or a number less than 6.

Verified step by step guidance

1. Identify the total number of equally likely outcomes. Since the spinner is divided into 8 regions numbered 1 through 8, the total number of outcomes is 8.
2. Determine the set of outcomes that satisfy the condition 'odd number'. The odd numbers between 1 and 8 are 1, 3, 5, and 7.
3. Determine the set of outcomes that satisfy the condition 'number less than 6'. These numbers are 1, 2, 3, 4, and 5.
4. Find the union of the two sets (odd numbers or numbers less than 6). This means combining all unique numbers from both sets: {1, 2, 3, 4, 5, 7}.
5. Calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. The probability is the size of the union set divided by 8.

Key Concepts

Probability of Equally Likely Outcomes

When all outcomes in a sample space are equally likely, the probability of an event is the ratio of favorable outcomes to the total number of outcomes. For example, with 8 equally likely sections on a spinner, the probability of landing on any one section is 1/8.

Union of Events (OR Probability)

The probability of either event A or event B occurring is found by adding their individual probabilities and subtracting the probability of both occurring together. This avoids double-counting outcomes that satisfy both conditions.

Identifying Event Sets Based on Conditions

To solve probability problems, it is essential to correctly identify the sets of outcomes that meet given conditions, such as 'odd numbers' or 'numbers less than 6.' This helps in determining the favorable outcomes for calculating probabilities.