Let's solve this problem step-by-step.

Problem Summary

We're asked to find the probability that a randomly chosen integer between 1 and 10 (inclusive) will be either:

1. Greater than 5, or
2. An odd number.

Let's denote:

• Event $A$ as the event that the number is greater than 5.
• Event $B$ as the event that the number is odd.

Step 1: Identify Numbers for Each Event

1. Event $A$: Numbers greater than 5

   • The integers greater than 5 within the range 1 to 10 are: $6, 7, 8, 9,$ and $10$.
   • So, there are 5 numbers in this set.

2. Event $B$: Odd numbers

   • The odd integers within the range 1 to 10 are: $1, 3, 5, 7,$ and $9$.
   • So, there are 5 numbers in this set as well.

Step 2: Find the Overlap (Intersection) of Events $A$ and $B$

• The numbers that are both greater than 5 and odd are: $7$ and $9$.
• There are 2 numbers in this intersection set.

Step 3: Calculate the Probability Using the Addition Rule

The probability of either event $A$ or $B$ occurring is given by: $P(A \cup B) = P(A) + P(B) - P(A \cap B)$ where:

• $P(A) = \frac{5}{10}$,
• $P(B) = \frac{5}{10}$,
• $P(A \cap B) = \frac{2}{10}$.

So, $P(A \cup B) = \frac{5}{10} + \frac{5}{10} - \frac{2}{10} = \frac{8}{10} = \frac{4}{5}.$

Answer

The correct probability that the number chosen will be more than 5 or odd is: $\frac{4}{5}$

Would you like further details, or do you have questions?

Related Questions

1. What is the probability that a number chosen is less than 5 or even?
2. If the range is extended from 1 to 20, how would the probability change?
3. How do we calculate probabilities when dealing with more complex overlaps?
4. What is the probability of selecting a number that is exactly divisible by 3?
5. How would the answer change if only odd numbers could be chosen?

Tip

When calculating probabilities involving "or" statements, remember to account for any overlap to avoid double-counting.