A fair die is thrown twice. What is the probability that the product of the two numbers obtained is even?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\frac{3}{4}\)
A product is odd only when both numbers are odd; if either number is even, the product is even. So P(even product) \(=1-\) P(both odd).
Odd faces: 1, 3, 5, so P(odd on one throw) \(\displaystyle =\frac{3}{6}=\frac{1}{2}\)
P(both odd) \(\displaystyle =\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}\)
P(even product) \(\displaystyle =1-\frac{1}{4}=\frac{3}{4}\)