Worksheet 1Worksheet 2Worksheet 3

The download includes this worksheet followed by the answer key with explanations. In the print dialog choose “Save as PDF” to download.

lessonbunny.com
Name: ______________________________ Date: ______________

Compound Probability

Grade 7 · Statistics · Worksheet 3

  1. Emma is conducting a probability experiment with a bag of marbles and a standard six-sided die. The bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. Emma will randomly draw one marble from the bag and roll the die once. What is the probability that she draws a blue marble AND rolls a number greater than 4? Express your answer as a simplified fraction. Answer: ______________
  2. Emma is conducting a probability experiment with two spinners. The first spinner has 6 equal sections labeled with the numbers 1 through 6. The second spinner has 5 equal sections labeled with the letters A, B, C, D, and E. If Emma spins both spinners once, what is the probability that she gets an even number on the first spinner AND a vowel on the second spinner? Express your answer as a simplified fraction. Answer: ______________
  3. P(red) = 3/8, P(blue) = 1/4, P(red or blue) = ? Answer: ______________
  4. P(red or blue) = 3/10 + 1/5 = ? Answer: ______________
  5. Emma is conducting a probability experiment with a bag of marbles and a spinner. The bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. The spinner has 4 equal sections labeled 1, 2, 3, and 4. If Emma randomly draws one marble from the bag and spins the spinner once, what is the probability that she draws a blue marble AND the spinner lands on an even number? Answer: ______________
  6. Emma is conducting a probability experiment with a bag of marbles and a standard six-sided die. The bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. She randomly draws one marble from the bag and rolls the die once. What is the probability that Emma draws a blue marble AND rolls a number greater than 4? Express your answer as a simplified fraction. Answer: ______________
  7. P(red) = 3/10, P(blue) = 1/4, P(red or blue) = ? Answer: ______________
lessonbunny.com

Answer Key & Explanations

Compound Probability · Grade 7 · Worksheet 3

  1. Emma is conducting a probability experiment with a bag of marbles and a standard six-sided die. The bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. Emma will randomly draw one marble from the bag and roll the die once. What is the probability that she draws a blue marble AND rolls a number greater than 4? Express your answer as a simplified fraction. Answer: 1/15 Solution: Find the probability of drawing a blue marble. There are 2 blue marbles out of 3 + 2 + 5 = 10 total marbles.
    Full step-by-step solution

    Step 1: Find the probability of drawing a blue marble. There are 2 blue marbles out of 3 + 2 + 5 = 10 total marbles. Probability of blue marble = 2/10 = 1/5 Step 2: Find the probability of rolling a number greater than 4 on a six-sided die. Numbers greater than 4 are 5 and 6. Probability of number > 4 = 2/6 = 1/3 Step 3: Since these are independent events, multiply the probabilities. Probability of both events = (1/5) × (1/3) = 1/15 The answer is 1/15.

  2. Emma is conducting a probability experiment with two spinners. The first spinner has 6 equal sections labeled with the numbers 1 through 6. The second spinner has 5 equal sections labeled with the letters A, B, C, D, and E. If Emma spins both spinners once, what is the probability that she gets an even number on the first spinner AND a vowel on the second spinner? Express your answer as a simplified fraction. Answer: 1/5 Solution: Find the probability of getting an even number on the first spinner. The first spinner has numbers 1, 2, 3, 4, 5, 6. Even numbers are 2, 4, 6.
    Full step-by-step solution

    Step 1: Find the probability of getting an even number on the first spinner. The first spinner has numbers 1, 2, 3, 4, 5, 6. Even numbers are 2, 4, 6. So there are 3 favorable outcomes out of 6 total sections. Probability = 3/6 = 1/2 Step 2: Find the probability of getting a vowel on the second spinner. The second spinner has letters A, B, C, D, E. Vowels are A and E. So there are 2 favorable outcomes out of 5 total sections. Probability = 2/5 Step 3: Find the probability of both events occurring. For independent events, multiply the probabilities. Probability = (1/2) × (2/5) = 2/10 = 1/5 The answer is 1/5.

  3. P(red) = 3/8, P(blue) = 1/4, P(red or blue) = ? Answer: 5/8 Solution: Identify the given probabilities: P(red) = 3/8, P(blue) = 1/4 Convert 1/4 to eighths to match denominators: 1/4 = 2/8 Since these are mutually exclusive events (cannot both happen at the same time), add the probabilities: 3/8 + 2/8 = 5/8 The probability of drawing red or blue is 5/8 The answer…
    Full step-by-step solution

    Step 1: Identify the given probabilities: P(red) = 3/8, P(blue) = 1/4 Step 2: Convert 1/4 to eighths to match denominators: 1/4 = 2/8 Step 3: Since these are mutually exclusive events (cannot both happen at the same time), add the probabilities: 3/8 + 2/8 = 5/8 Step 4: The probability of drawing red or blue is 5/8 The answer is 5/8.

  4. P(red or blue) = 3/10 + 1/5 = ? Answer: 1/2 Solution: P(red or blue) = 3/10 + 1/5 This means we are adding two probabilities. The first fraction is 3/10. The second fraction is 1/5.
    Full step-by-step solution

    Step 1: Understand the problem We are given: P(red or blue) = 3/10 + 1/5 This means we are adding two probabilities. Step 2: Check if the fractions have the same denominator The first fraction is 3/10. The second fraction is 1/5. Since the denominators are different (10 and 5), we cannot add them directly. Step 3: Find a common denominator The least common denominator of 10 and 5 is 10. We convert 1/5 to a fraction with denominator 10: 1/5 = (1 × 2)/(5 × 2) = 2/10. Step 4: Add the fractions Now we have: 3/10 + 2/10 = (3 + 2)/10 = 5/10. Step 5: Simplify the result 5/10 can be simplified by dividing numerator and denominator by 5: 5 ÷ 5 = 1, 10 ÷ 5 = 2, so 5/10 = 1/2. Step 6: Final answer P(red or blue) = 1/2.

  5. Emma is conducting a probability experiment with a bag of marbles and a spinner. The bag contains 3 red marbles, 2 blue marbles, and 5 green marbles. The spinner has 4 equal sections labeled 1, 2, 3, and 4. If Emma randomly draws one marble from the bag and spins the spinner once, what is the probability that she draws a blue marble AND the spinner lands on an even number? Answer: 1/10 Solution: Find the probability of drawing a blue marble. There are 2 blue marbles out of 3 + 2 + 5 = 10 total marbles. Probability(blue marble) = 2/10 = 1/5.
    Full step-by-step solution

    Step 1: Find the probability of drawing a blue marble. There are 2 blue marbles out of 3 + 2 + 5 = 10 total marbles. Probability(blue marble) = 2/10 = 1/5. Step 2: Find the probability of the spinner landing on an even number. The even numbers on the spinner are 2 and 4. There are 2 favorable outcomes out of 4 total sections. Probability(even number) = 2/4 = 1/2. Step 3: Find the probability of both events happening. Since the events are independent, multiply the individual probabilities. Probability(blue AND even) = (1/5) × (1/2) = 1/10. The answer is 1/10.

  6. Emma is conducting a probability experiment with a bag of marbles and a standard six-sided die. The bag contains 5 red marbles, 3 blue marbles, and 2 green marbles. She randomly draws one marble from the bag and rolls the die once. What is the probability that Emma draws a blue marble AND rolls a number greater than 4? Express your answer as a simplified fraction. Answer: 1/10 Solution: Find the probability of drawing a blue marble. Total marbles = 5 red + 3 blue + 2 green = 10 marbles Blue marbles = 3 Probability of blue marble = 3/10 Find the probability of rolling a number greater than 4 on a six-sided die.
    Full step-by-step solution

    Step 1: Find the probability of drawing a blue marble. Total marbles = 5 red + 3 blue + 2 green = 10 marbles Blue marbles = 3 Probability of blue marble = 3/10 Step 2: Find the probability of rolling a number greater than 4 on a six-sided die. Numbers greater than 4: 5 and 6 Favorable outcomes = 2 Total possible outcomes = 6 Probability = 2/6 = 1/3 Step 3: Find the probability of both events occurring. Since these are independent events, multiply the probabilities: (3/10) × (1/3) = 3/30 = 1/10 The answer is 1/10.

  7. P(red) = 3/10, P(blue) = 1/4, P(red or blue) = ? Answer: 11/20 Solution: Write down the given probabilities: P(red) = 3/10, P(blue) = 1/4 Since these are mutually exclusive events (a marble cannot be both red and blue), we add the probabilities: P(red or blue) = P(red) + P(blue) Convert fractions to have a common denominator: 3/10 = 6/20, 1/4 = 5/20 Add the…
    Full step-by-step solution

    Step 1: Write down the given probabilities: P(red) = 3/10, P(blue) = 1/4 Step 2: Since these are mutually exclusive events (a marble cannot be both red and blue), we add the probabilities: P(red or blue) = P(red) + P(blue) Step 3: Convert fractions to have a common denominator: 3/10 = 6/20, 1/4 = 5/20 Step 4: Add the fractions: 6/20 + 5/20 = 11/20 Step 5: The probability of drawing either a red or blue marble is 11/20.