Q1. What is the probability of drawing a heart from a standard deck of 52 cards?

Background

Topic: Basic Probability

This question tests your understanding of calculating probabilities for simple events in a uniform sample space, such as drawing a card from a deck.

Key Terms and Formulas

• Probability of an event :

• Standard deck: 52 cards, 4 suits (hearts, diamonds, clubs, spades), 13 cards per suit.

Step-by-Step Guidance

1. Identify the total number of possible outcomes: There are 52 cards in a standard deck.

2. Determine the number of favorable outcomes: There are 13 hearts in the deck.

3. Set up the probability formula:

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Q2. If two dice are rolled, what is the probability that the sum is 7?

Background

Topic: Probability with Multiple Events

This question tests your ability to count outcomes and calculate probabilities for compound events (rolling two dice).

Key Terms and Formulas

• Sample space for two dice: 36 possible outcomes (6 sides on each die).

• Probability:

Step-by-Step Guidance

1. List all possible pairs of dice rolls that sum to 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).

2. Count the number of favorable outcomes (pairs that sum to 7).

3. Set up the probability formula:

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Q3. A box contains 5 red balls and 7 blue balls. If one ball is drawn at random, what is the probability it is blue?

Background

Topic: Probability with Counting

This question tests your ability to calculate probabilities when outcomes are not equally divided (different numbers of red and blue balls).

Key Terms and Formulas

• Total balls: 5 red + 7 blue = 12 balls.

• Probability:

Step-by-Step Guidance

1. Count the total number of balls in the box.

2. Identify the number of blue balls.

3. Set up the probability formula:

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Q4. If a coin is tossed three times, what is the probability of getting exactly two heads?

Background

Topic: Binomial Probability

This question tests your understanding of binomial probability, where you count the number of ways to get a certain number of successes in repeated independent trials.

Key Terms and Formulas

• Number of trials (): 3

• Number of successes (): 2

• Probability of head (): 0.5

• Binomial probability formula:

Step-by-Step Guidance

1. Identify , , .

2. Calculate the number of ways to get 2 heads in 3 tosses: .

3. Set up the binomial probability formula:

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Q5. A multiple-choice test has 4 questions, each with 3 possible answers. If a student guesses on all questions, what is the probability of getting all answers correct?

Background

Topic: Probability of Independent Events

This question tests your understanding of the multiplication rule for independent events.

Key Terms and Formulas

• Probability of guessing one question correctly:

• Probability of all correct:

Step-by-Step Guidance

1. Identify the probability of guessing one question correctly:

2. Since the questions are independent, multiply the probability for each question:

Try solving on your own before revealing the answer!