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Probability: Possible Values

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Q1. The function g: [-a,a] --> R, g(x) = sin(2(x-pi/6)) has an inverse function. The maximum possible value is a is:_____.

Q2. Harry is a soccer player who practices penalty kicks many times each day. Each time Harry takes a penalty kick, the probability that he scores a goal is 0.7, independent of any other penalty kick. One day Harry took 20 penalty kicks. Given that he scored at least 12 goals, the probability that Harry scored exactly 15 goals is closest to ____.

Q3. For events A and B, Pr(A intersection B) = p, Pr(A' intersection B) = P - 1/8 and Pr(A intersection B') = 3p/5. If A and B are independent, then the value of p is ___.

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This solution provide step by step solutions to some probability questions.

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Q1. The function g: [-a,a] --> R, g(x) = sin(2(x-pi/6)) has an inverse function. The maximum possible value is a is:_____.

Solution:

x - sin(2(y-pi/6))
sin^-1x = 2(y-pi/6)
y - pi/6 = 1/2 sin^-1x
y = 1/2sin^-1x + pi/6
g^-1(x) = 1/2sin^-1x + pi/6

Maximum value of a will be when is sin^-1x is pi/2
Thus, a = ...

Solution provided by:
Sandhya Sharma, MSc
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  • BSc, Meerut University
  • MSc, Meerut University
  • MPhil, Institute of Advanced Studies
  • MSc, AIT
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