Question 1: Calculate the expected number of red balls drawn in 60 draws if the probability of drawing a red ball is 1/4.

Answer: 15

Question 2: If a spinner with 8 equal sections (3 green, 2 blue, 3 yellow) is spun 40 times, what is the expected number of yellow spins?

Answer: 15

Question 3: Determine the expected frequency of heads if a fair coin is tossed 120 times.

Answer: 60

Question 1: A survey shows that 60% of students like chocolate ice cream. If 50 students are surveyed, estimate how many students are expected to like chocolate ice cream. Explain your reasoning.

Answer: 30 students; Expected = 50 × 0.6 = 30

Question 2: A bag contains 5 red, 3 blue, and 2 green marbles. If 20 marbles are drawn with replacement, what is the expected number of green marbles drawn? Provide your calculation.

Answer: Expected green = 20 × (2/10) = 4

Question 3: A class has 24 students: 10 boys and 14 girls. If a student is chosen at random, what is the expected number of girls in a group of 4 students selected? Explain your approach.

Answer: Expected girls = 4 × (14/24) ≈ 2.33

Question 1: A factory produces 100 light bulbs daily, of which 10 are defective. What is the expected number of defective bulbs in 7 days? Show your calculations.

Answer: Expected defectives = 7 × 10 = 70

Question 2: A survey indicates that 25% of customers prefer brand A. If 80 customers shop in a day, how many are expected to prefer brand A? Provide reasoning.

Answer: Expected = 80 × 0.25 = 20

Question 3: A deck of 52 cards has 13 hearts. If 12 cards are drawn at random with replacement, what is the expected number of hearts drawn? Show your work.

Answer: Expected hearts = 12 × (13/52) = 3

Question 1: A lottery has a 1 in 100 chance of winning. If 500 tickets are sold, what is the expected number of winners? Explain your steps.

Answer: Expected winners = 500 × (1/100) = 5

Question 2: A survey shows 40% of people prefer tea over coffee. Out of 150 people surveyed, estimate how many prefer tea. Then, suppose 200 people are surveyed, what is the new expected number? Show your calculations and discuss any assumptions.

Answer: First: 150 × 0.4 = 60; Second: 200 × 0.4 = 80

Question 1: Plot the expected frequency of rolling a 4 on a fair six-sided die after 60 rolls.

Answer: Expected = 60 × (1/6) = 10

Question 2: Construct a bar graph showing the expected number of students liking different fruits: apples (30), oranges (45), bananas (25). Use the grid to draw.

Answer: Students expected liking each fruit as given; students draw bars accordingly.

Question 3: A spinner with 5 equal sections (red, blue, green, yellow, purple). If spun 100 times, what is the expected number of green spins? Show your work.

Answer: Expected = 100 × (1/5) = 20

Question 1: A student calculates the expected number of defective products as 10 out of 100, then multiplies by 7 days: 10 × 7 = 70. Is this correct? Explain and correct if needed.

Answer: Incorrect; Expected per day is 10, so over 7 days it's 10 × 7 = 70, which is correct. No correction needed.

Question 2: A student forgets to divide the total number of favorable outcomes by total outcomes when calculating expected frequency. Describe the mistake and how to fix it.

Answer: Mistake: Not calculating probability. Fix by dividing favorable outcomes by total outcomes to find probability before multiplying by total trials.