Here are the solutions to the exercises in the image:

1. Write everything you know currently about probability.

Probability is the measure of how likely an event is to occur. It is calculated using the formula:
$P(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}$

• Probability values range from 0 to 1.
• If P(A) = 0, the event is impossible.
• If P(A) = 1, the event is certain.
• The sum of probabilities of all possible outcomes of an experiment is always 1.

2. Give the sample space for each experiment.

(a) Choosing an odd number between 1 and 11 at random:
Sample space: {1, 3, 5, 7, 9, 11}

(b) Choosing a prime number less than 15 at random:
Sample space: {2, 3, 5, 7, 11, 13}

(c) Choosing one candy at random from a small bag containing 5 red, 7 blue, and 2 green candies:
Sample space: {Red, Blue, Green}

(d) Choosing 1 letter at random from 5 vowels:
Sample space: {A, E, I, O, U}

(e) Choosing 1 letter at random from the word "divide":
Sample space: {D, I, V, I, D, E}

3. What is the probability of choosing a vowel from the English alphabet?

There are 5 vowels (A, E, I, O, U) and 26 letters in total.
$P(\text{vowel}) = \frac{5}{26}$

4. A number between 1 and 11 is chosen at random. What is the probability of choosing an odd number?

Odd numbers between 1 and 11: {1, 3, 5, 7, 9, 11} (6 numbers)
Total numbers: 11
$P(\text{odd}) = \frac{6}{11}$

5. What is the probability of choosing 14 hearts from a standard deck of 52 playing cards?

A standard deck has 13 hearts. It is impossible to choose 14 hearts, so:
$P(\text{choosing 14 hearts}) = 0$

6. Which of the following numbers cannot be the probability of some event?

Probability must be between 0 and 1 (inclusive). Any number outside this range is not valid.

• (a) 0 ✅ (Valid)
• (b) 1 ✅ (Valid)
• (c) 1.3 ❌ (Invalid, greater than 1)
• (d) 0.71 ✅ (Valid)
• (e) -0.5 ❌ (Invalid, negative)
• (f) 2.1 ❌ (Invalid, greater than 1)
• (g) 0.5 ✅ (Valid)
• (h) 120 ❌ (Invalid, greater than 1)
• (i) 105% ❌ (Invalid, as 105% = 1.05 > 1)
• (j) 0.67 ✅ (Valid)

Invalid options: (c), (e), (f), (h), (i)

7. If a number is chosen at random from the following list, what is the probability that it is a prime?

Given list: {2, 3, 5, 7, 11, 13, 17, 19}

• All 8 numbers are prime.
• Total numbers in the list: 8
  $P(\text{prime}) = \frac{8}{8} = 1$

Do you want more details or explanations? Let me know!

5 Related Questions to Explore:

1. What is the difference between theoretical and experimental probability?
2. How do you calculate probability when dealing with independent and dependent events?
3. What is the probability of drawing an Ace from a deck of 52 playing cards?
4. If two dice are rolled, what is the probability of getting a sum of 7?
5. What is the probability of drawing a red card from a standard deck of 52 playing cards?

Tip:

Always check if probabilities add up to 1 in a given sample space. If they don’t, something might be missing! 🚀