Probability of a Student Being a Senior
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Questions and Answers

In the context of the text, what is the approximate probability that no two people in a group of seven have the same birthday?

  • 0.92
  • 0.94
  • 0.43
  • 0.056 (correct)
  • When finding the limit of (sin 3x) / (sin 4x) as x approaches 0, what is the result?

  • 1 (correct)
  • 0
  • 2
  • 3/4
  • If a shipment of 12 television sets contains 3 defective sets, in how many ways can a hotel purchase 5 sets and receive at least 2 of the defective sets?

  • 288 ways, 144 ways
  • 210 ways, 140 ways
  • 240 ways, 110 ways (correct)
  • 152 ways, 228 ways
  • For x = 2 sin θ and y = cos 2θ, what is d²y/dx²?

    <p>-cot θ / cos θ</p> Signup and view all the answers

    What is the probability of getting either two heads or three heads when six fair coins are tossed at once?

    <p>0.35</p> Signup and view all the answers

    In the federal prison, if 3/5 of the inmates are male and 5/8 are female or 25 years of age or older, what is the probability of selecting a female inmate who is at least 25 years old?

    <p>15/120</p> Signup and view all the answers

    If f(a) = f(b) = 0 and f(x) is continuous on [a, b], what can be concluded about f(x)?

    <p>f(x) must be identically zero</p> Signup and view all the answers

    Regarding the inequality between mean and variance of the Binomial distribution, which statement is true?

    <p>Mean &lt; Variance</p> Signup and view all the answers

    If a student is randomly chosen from the class and found to have earned an A, what is the probability that he or she is a junior?

    <p>0.48</p> Signup and view all the answers

    What is the derivative of y = (x + 1)ln²(x + 1) with respect to x?

    <p>2ln(x + 1) + 4ln²(x + 1)</p> Signup and view all the answers

    What is the probability that a student arranges the cards in the order blue, red, yellow, and green, given that they have 6 color options and choose randomly?

    <p>1/540</p> Signup and view all the answers

    What is the integral of (2x + 1)/(4 + x²) dx?

    <p>(1/2) tan¯¹ (x/2) + C</p> Signup and view all the answers

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