MDM4U Chapter 5: Probability Distributions Review
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Questions and Answers

What is the expected number of King’s runners in the first heat?

  • 1.25 (correct)
  • 4
  • 0
  • 2

    • What is the probability that there will be more than 1 King’s student in the first heat?

  • 0.1813186813
  • 0.4532967033
  • 0.3653846154 (correct)
  • 0.3021978022

    • What is the probability of getting exactly 2 fours in 5 die tosses?

  • 0.1607510288 (correct)
  • 0.0625
  • 0.208896
  • 0.3021978022

    • What is the probability that all four of the Smiths' children will be boys?

    <p>0.0625</p> Signup and view all the answers

    If a batter has a 0.320 batting average, what is the probability they get exactly 1 hit in 3 chances?

    <p>0.443904</p> Signup and view all the answers

    What is the expected number of hits per game if a batter has a 0.320 batting average?

    <p>0.96</p> Signup and view all the answers

    If the Smiths have four children, what is the probability that at least two of them will be girls?

    <p>0.6875</p> Signup and view all the answers

    How many chances does a player get per game if they have a probability distribution for number of hits given?

    <p>3</p> Signup and view all the answers

    What is the probability that it takes him 5 at bats?

    <p>0.0641105763</p> Signup and view all the answers

    What is the probability that it takes him less than 4 at bats?

    <p>0.715109688</p> Signup and view all the answers

    What is the probability that the first defective circuit board will be the sixth one tested?

    <p>0.0212549619</p> Signup and view all the answers

    What is the probability that the first defective circuit board will be among the first six tested?

    <p>0.1356315509</p> Signup and view all the answers

    What is the expected number of circuit boards that would have to be tested until finding a defective one?

    <p>41.67</p> Signup and view all the answers

    Using Pascal’s Identity, which of the following expressions simplifies correctly?

    <p>$\binom{n+1}{r} = \binom{n}{r-1} + \binom{n}{r}$</p> Signup and view all the answers

    What is the expected value of the number of bad apples drawn from the basket of 12 apples?

    <p>1.666667</p> Signup and view all the answers

    What is the probability of drawing at least one face card in a 5-card hand from a standard deck of 52 cards?

    <p>0.7468187275</p> Signup and view all the answers

    In a hypergeometric probability distribution, what is the probability of drawing a specific number of success outcomes?

    <p>Depending on the number of trials</p> Signup and view all the answers

    What is the expected value of the number of face cards drawn in a 5-card hand from a standard deck of 52 cards?

    <p>1.153846154</p> Signup and view all the answers

    What is the probability distribution of the number of bad apples drawn from a basket of 12 apples?

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

    What is the probability of drawing 2 face cards in a 5-card hand from a standard deck of 52 cards?

    <p>0.2509003601</p> Signup and view all the answers

    What is the probability distribution of the number of students from King’s running in the first heat?

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

    What is the expected value of the number of students from King’s running in the first heat?

    <p>1.25</p> Signup and view all the answers

    What is the probability that a customer at Fiona’s Fine Foods takes exactly 5 minutes?

    <p>0.2483660131</p> Signup and view all the answers

    What is the expected length of a typical sale at Fiona’s Fine Foods?

    <p>5.49</p> Signup and view all the answers

    What is the probability of winning $500 in the school fundraising lottery?

    <p>$\frac{1}{400}$</p> Signup and view all the answers

    What is the expected value of a ticket in the school fundraising lottery?

    <p>12.425</p> Signup and view all the answers

    What would be your expected loss if you buy one lottery ticket for $25?

    <p>−12.575</p> Signup and view all the answers

    What is the probability that a randomly selected high school student speaks three languages?

    <p>0.065</p> Signup and view all the answers

    What is the validity criterion for the probability distribution of languages spoken by high school students?

    <p>The sum of all probabilities is equal to 1.</p> Signup and view all the answers

    What is the expected number of languages spoken by a randomly selected high school student if probabilities are: $P(1) = 0.630$, $P(2) = 0.295$, $P(3) = 0.065$, $P(4) = 0.008$, $P(5) = 0.002$?

    <p>1.88</p> Signup and view all the answers

    What is the probability that Pitu gets all 10 questions right?

    <p>0.00390625</p> Signup and view all the answers

    If you buy ten cups of coffee with a 20% chance of winning a prize per cup, what is the expected number of prizes you would win?

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

    In a batch of 100 computer chips with a 0.9% defect rate, what is the probability that exactly 1 chip is defective?

    <p>0.3677344383</p> Signup and view all the answers

    What is the probability that at least 3 out of 100 computer chips are defective if the defect rate is 0.9%?

    <p>0.0620355717</p> Signup and view all the answers

    In Monopoly, if the only way to get out of jail is rolling doubles, what is the probability that it takes more than 3 turns to roll doubles?

    <p>0.5787037037</p> Signup and view all the answers

    How many attempts would you expect to have to roll the dice to get doubles once in Monopoly?

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

    What is the probability that less than 5 out of 100 computer chips are defective with a 0.9% defect rate?

    <p>0.9978089603</p> Signup and view all the answers

    What is the probability that Pitu gets at least eight questions right if $P(X ext{>=} 2)$ is 0.26171875?

    <p>0.26171875</p> Signup and view all the answers

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