Solution: 2015 Winter Final - 17
Author: Michiel SmidQuestion
Consider a uniformly random bitstring of length 5. Define the events
- A = "the bitstring contains exactly two 0s",
- B = "the bitstring contains an even number of 0s".
(a)
$\left. 2^5 \middle/ {5 \choose 2} \right.$
(b)
$\left. {5 \choose 2} \middle/ 2^3 \right.$
(c)
$\left. {5 \choose 2} \middle/ 2^5 \right.$
(d)
$\left. {5 \choose 2} \middle/ 2^4 \right.$
Solution
- Let's determine B
$ |B| = 2^4 $ - Let's determine $ A = A \cap B $
$ |A| = \binom{5}{2} $ - $ Pr(A|B) = \frac{Pr(A \cap B)}{Pr(B)} $
$ Pr(A|B) = \frac{\binom{5}{2}}{2^4} $