Discrete Probability Distributions Chapter 5
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Questions and Answers

What is the probability of a success in a Bernoulli trial?

  • 33%
  • 75%
  • 50%
  • 25% (correct)

    • What is the number of successes in a Bernoulli process called?

  • Poisson random variable
  • Geometric random variable
  • Bernoulli random variable
  • Binomial random variable (correct)

    • How many possible outcomes are there in a set of three Bernoulli trials?

  • 6
  • 8 (correct)
  • 4
  • 10

    • What is the probability of the outcome NDN in a set of three Bernoulli trials?

    <p>9/46</p> Signup and view all the answers

    What is the value of X in the outcome DDN?

    <p>2</p> Signup and view all the answers

    What is the characteristic of a Bernoulli process that ensures the probability of success remains constant?

    <p>The probability of success remains constant from trial to trial</p> Signup and view all the answers

    What is the probability distribution of a discrete random variable called?

    <p>Binomial distribution</p> Signup and view all the answers

    What is the probability of a failure in a Bernoulli trial, given the probability of success is p?

    <p>1 - p</p> Signup and view all the answers

    What is the formula for the binomial distribution of a random variable X, where X is the number of successes in n independent trials?

    <p>b(x; n, p) = (n choose x) p^x q^(n-x)</p> Signup and view all the answers

    What is the probability that exactly 2 of the next 4 components tested will survive, given that the probability of a component surviving a shock test is 3/4?

    <p>27/128</p> Signup and view all the answers

    What is the probability distribution of the number of defective devices among 20 items, given that the defective rate of the device is 3%?

    <p>b(x; 20, 0.03)</p> Signup and view all the answers

    What is the probability that there will be at least one defective item among 20 items, given that the defective rate of the device is 3%?

    <p>1 - (0.97)^20</p> Signup and view all the answers

    What is the probability that a patient recovers from a rare blood disease?

    <p>0.4</p> Signup and view all the answers

    What is the probability that exactly 5 people survive if 15 people are known to have contracted the rare blood disease?

    <p>0.1859</p> Signup and view all the answers

    What is the probability that at least 10 people survive if 15 people are known to have contracted the rare blood disease?

    <p>0.0338</p> Signup and view all the answers

    What is the probability that from 3 to 8 people survive if 15 people are known to have contracted the rare blood disease?

    <p>0.1859</p> Signup and view all the answers

    What is the mean of the binomial random variable in the given scenario?

    <p>6</p> Signup and view all the answers

    What is the variance of the binomial random variable in the given scenario?

    <p>3.6</p> Signup and view all the answers

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