Let's break down the questions one by one based on the image you provided.

Question 1

For the set of numbers: $1, 2, 5, 5, 8, 9, 10, 5, 3, 8$

(a) List them in ascending order: The numbers in ascending order are: $1, 2, 3, 5, 5, 5, 8, 8, 9, 10$

(b) How many numbers are in the set? There are 10 numbers in the set.

(c) Calculate the:

• i. Mean: The mean is calculated as the sum of the numbers divided by the count: $\text{Mean} = \frac{1 + 2 + 3 + 5 + 5 + 5 + 8 + 8 + 9 + 10}{10} = \frac{56}{10} = 5.6$
• ii. Mode: The mode is the most frequent number in the set. The number 5 appears the most (3 times). $\text{Mode} = 5$
• iii. Median: The median is the middle value of the set. Since there are 10 numbers (even count), the median is the average of the 5th and 6th numbers: $\text{Median} = \frac{5 + 5}{2} = 5$
• iv. Range: The range is the difference between the largest and smallest numbers: $\text{Range} = 10 - 1 = 9$

(d) If each number in the set is doubled, what is the new mean? Doubling all the numbers doubles the sum. The new sum is $56 \times 2 = 112$, and the count remains the same (10). $\text{New Mean} = \frac{112}{10} = 11.2$

Question 2

There are four spinners labeled A, B, C, D, each with different numbers.

(a) Which spinner has the lowest probability of landing on the number 1 in a single spin?

• Spinner D has 6 sections, and only 1 of them is the number 1, so the probability is $\frac{1}{6}$, which is the lowest probability.

(b) Which spinner has a 50% probability of landing on the number 1 in a single spin?

• Spinner B has 2 sections, and one of them is the number 1. The probability is $\frac{1}{2}$ or 50%.

(c) List the spinners in order, from the most likely to land on the number 1 to the least likely:

• Spinner B: $\frac{1}{2}$
• Spinner C: $\frac{1}{3}$
• Spinner A: $\frac{1}{4}$
• Spinner D: $\frac{1}{6}$

Question 3

This question is about the probability of drawing specific cards from a standard 52-card deck.

(a) Probability of drawing a red card: There are 26 red cards (hearts and diamonds). $P(\text{red}) = \frac{26}{52} = \frac{1}{2}$

(b) Probability of drawing a black card: There are 26 black cards (spades and clubs). $P(\text{black}) = \frac{26}{52} = \frac{1}{2}$

(c) Probability of drawing a heart: There are 13 hearts in the deck. $P(\text{heart}) = \frac{13}{52} = \frac{1}{4}$

(d) Probability of drawing an ace: There are 4 aces in the deck. $P(\text{ace}) = \frac{4}{52} = \frac{1}{13}$

(e) Probability of drawing a king: There are 4 kings in the deck. $P(\text{king}) = \frac{4}{52} = \frac{1}{13}$

(f) Probability of drawing a red 7: There are 2 red 7s (one in hearts and one in diamonds). $P(\text{red 7}) = \frac{2}{52} = \frac{1}{26}$

Would you like any more details or explanations for any of these problems?

Here are some additional practice questions:

1. If the set of numbers in Question 1 had an additional number, 6, how would the mean change?
2. If a spinner has 8 sections, how would the probability of landing on a specific number compare with the spinners in Question 2?
3. What is the probability of drawing a face card (jack, queen, or king) from a standard deck?
4. If each number in the set in Question 1 is multiplied by 3, what would the new mean and range be?
5. How would the mode of the set in Question 1 change if another 8 were added?

Tip: When working with probabilities, it's often helpful to reduce fractions to their simplest form to better compare outcomes!