Question

A box contains five blocks numbered 1, 2,
3, 4, and 5. John picks a block and replaces it. Lisa then picks a block. What is the probability that the sum of the numbers they picked is even?

Answer 1

If both pick odd numbered blocks the sum will be even. If both pick even numbered blocks the sum will also be even.
P(odd) = 3/5
\[\large P(odd \cap odd)=\frac{3}{5}\times\frac{3}{5}\]
\[\large P(even \cap even)=\frac{2}{5}\times\frac{2}{5}\]
The events 'both pick odd' and 'both pick even' are mutually exclusive, therefore the probabilities of these event must be added to find the probability that the sum of the numbers they picked is even.