A coin is tossed and a die is thrown. The probability that the outcome will be a tail on the coin or a number greater than 3 on the die is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{3}{4}\)
Let A be the event of a tail on the coin and B the event of a number greater than 3 (4, 5 or 6) on the die. The coin and the die do not affect each other, so A and B are independent:
\( \displaystyle P(A) = \frac{1}{2},\quad P(B) = \frac{3}{6} = \frac{1}{2} \)
\( \displaystyle P(A \cap B) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4} \)
By the addition rule,
\( \displaystyle P(A \cup B) = \frac{1}{2} + \frac{1}{2} - \frac{1}{4} = \frac{3}{4} \)
Shortcut: The event fails only with a head and a number 1, 2 or 3, with probability \(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}\). So the required probability is \(1 - \frac{1}{4} = \frac{3}{4}\).