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.

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.