A coin and six faced die, both unbiassed, are thrown simultaneously. The probability of getting a head on…
A coin and six faced die, both unbiassed, are thrown simultaneously. The probability of getting a head on the coin and an odd number on the die, is
$\frac{1}{2}$
$\frac{3}{4}$
$\frac{1}{4}$
$\frac{2}{3}$
Solution
Let $E=$ Event of getting a head from a coin.
$F=$ Event of getting an odd number $(1,3,5)$ from a die.
$P(E)=\frac{1}{2}, P(F)=\frac{3}{6}=\frac{1}{2}$
Since $E$ and $F$ are independent events
$\begin{aligned}
\therefore \quad P(E \cap F) & =P(E) \cap P(F) \\
& =\frac{1}{2} \times \frac{1}{2}=\frac{1}{4}
\end{aligned}$