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MathematicsSS 2en

🎲 Probability of Independent Events

Master the fundamental concepts and calculations for independent events in probability theory. **What you'll learn:** - Identify and distinguish independent events from dependent events - Calculate the probability of two or more independent events occurring - Apply the multiplication rule for independent events - Solve real-world problems involving compound independent events - Use tree diagrams and probability notation correctly

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Questions in this quiz

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  1. Question 1

    Two events A and B are independent if:

  2. Question 2

    Rolling a fair die and flipping a fair coin are independent events.

  3. Question 3

    If P(A)=0.4P(A) = 0.4 and P(B)=0.5P(B) = 0.5, and A and B are independent events, then P(A and B)=P(A \text{ and } B) = ___

  4. Question 4

    Drawing a card from a deck, replacing it, and then drawing another card are dependent events.

  5. Question 5

    A student has a probability of 23\frac{2}{3} of passing Mathematics and a probability of 34\frac{3}{4} of passing English. Assuming these are independent events, what is the probability of passing both subjects?

  6. Question 6

    A fair coin is flipped three times independently. The probability of getting heads all three times is (12)3=\left(\frac{1}{2}\right)^3 = ___

  7. Question 7

    Two fair dice are rolled simultaneously. What is the probability of rolling a 4 on the first die AND a 5 on the second die?

  8. Question 8

    If P(A)=0.3P(A) = 0.3, P(B)=0.7P(B) = 0.7, and A and B are independent, then P(A or B)=P(A)+P(B)=1.0P(A \text{ or } B) = P(A) + P(B) = 1.0.

  9. Question 9

    A bag contains 3 red balls and 2 blue balls. A ball is drawn, replaced, and another ball is drawn. What is the probability of drawing a red ball first AND a blue ball second?

  10. Question 10

    A student takes two independent tests. The probability of passing the first test is 45\frac{4}{5} and the probability of passing the second test is 35\frac{3}{5}. The probability of failing both tests is ___