Revision as of 21:23, 28 June 2024 by Admin (Created page with "A number <math>U</math> is chosen at random in the interval <math>[0,1]</math>. Find the probability that <math>T = U/(1 - U) < 1/4</math>. <ul class="mw-excansopts"> <li>1/6</li> <li>1/5</li> <li>1/4</li> <li>1/2</li> <li>2/3</li> </ul> '''References''' {{cite web |url=https://math.dartmouth.edu/~prob/prob/prob.pdf |title=Grinstead and Snell’s Introduction to Probability |last=Doyle |first=Peter G.|date=2006 |access-date=June 6, 2024}}")
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ABy Admin
Jun 28'24

Exercise

A number [math]U[/math] is chosen at random in the interval [math][0,1][/math]. Find the probability that [math]T = U/(1 - U) \lt 1/4[/math].

  • 1/6
  • 1/5
  • 1/4
  • 1/2
  • 2/3

References

Doyle, Peter G. (2006). "Grinstead and Snell's Introduction to Probability" (PDF). Retrieved June 6, 2024.

ABy Admin
Jun 28'24

Solution: B

[[math]]\frac{U}{1-U} \leq 1/4 \Leftrightarrow 4U \leq 1-U \Leftrightarrow U \leq 1/5[[/math]]

Hence the probability equals 1/5.

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