Question

I am bad at probability questions. Please help me?

Let `x` and `y` be uniformly distributed, independent random variable `[0,1]`. The probability that the minimum between `x` and `y` is less than `1/4` is
a) `1/16`
b) `7/16`
c) `1/2`
d) `5/16`

Answer 1

`"b) "7/16`

Explanation:

`"The opposite event is that the minimum is ">= 1/4`
`"It is more easy to calculate that event as we simply state"`
`"that x and y must both be ">= 1/4" then."`
`"And the odds for that are simply"`

`(3/4)^2 = 9/16`

`=> P["min "<= 1/4] = 1 - 9/16 = 7/16`