[Zeboy]

Two numbers are selected from the integers 1 to 11 inclusive, repetition being allowed.Find the probability that,
(a) Both are prime
(b) Both are powers of 2
(c) One is a prime and the other is a power of 2

[MathMaven53]

There are five primes between 1 and 11 inclusive:
2,3,5,7,11

The probability of picking any integer between 1 and 11
inclusive is 1/11 so the probability of picking a prime
between 1 and 11 inclusive is 5/11
Allowing for repetition; the probability of picking two
such primes is (5/11)^2 = 25/121

There are four powers of two between 1 and 11
inclusive. They are 1 = 2^0,2,4,84/11
So the probability of picking a such a power of
two is 4/11
Allowing for repetition; the probability of picking two
such powers of two is (4/11)^2 = 16/121

The probability of picking a prime and then a power of
two if these numbers lie between 1 and 11 inclusive and allowing for repetition is (5/11)(4/11)=20/121

[loloca]

The Probability That A Sloth Airlines Flight Will Be On Time Is 2/15. What Is The Probability That A Flight Will Be Late?

[Capuchin]

loloca, you might get an answer if you start your own post.

Asterisk, rating a post 3 years after it was posted! Classy! :p