A die is thrown and a coin is tossed. The probability that the outcome will be a number greater than 4 or a head or both is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \displaystyle\frac{2}{3} \)
Let A: the die shows more than 4 (5 or 6), and B: the coin shows a head. The die and the coin are independent.
\( \displaystyle P(A)=\frac{2}{6}=\frac{1}{3} \)
\( \displaystyle P(B)=\frac{1}{2} \)
\( \displaystyle P(A\cap B)=\frac{1}{3}\cdot\frac{1}{2}=\frac{1}{6} \)
\( \displaystyle P(A\cup B)=\frac{1}{3}+\frac{1}{2}-\frac{1}{6} \)
\( \displaystyle =\frac{2+3-1}{6}=\frac{2}{3} \)
Shortcut: The only unwanted outcomes are “4 or less” together with “tail”:
\( \displaystyle P(A\cup B)=1-\frac{4}{6}\cdot\frac{1}{2}=\frac{2}{3} \)