Two dice are thrown simultaneously. What is the probability that 4 will come up on at least one die?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\frac{11}{36}\)
“At least one 4” is the opposite of “no 4 on either die”, so its probability is 1 minus the probability of no 4. Two dice give \(6\times6=36\) equally likely outcomes.
Outcomes with no 4: each die shows one of the other 5 numbers, \(5\times5=25\)
P(no 4) \(\displaystyle =\frac{25}{36}\)
P(at least one 4) \(\displaystyle =1-\frac{25}{36}=\frac{11}{36}\)
Counted directly: 6 outcomes with 4 on the first die, 6 with 4 on the second, and (4, 4) is in both lists, so \(6+6-1=11\).