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#

1 Answer
Apr 26, 2018

#"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#