Question

A pair of fair dice having six faces numbered from 1 to 6 are thrown once, suppose two events
E and F are defined as
E : Product of the two numbers appearing is divisible by 5.
F : At least one of the dice shows up the face one.
Then the vents E and F are

• A. mutually exclusive
• B. independent
• C. neither independent nor mutually exclusive
• D. are equiprobable

Answer 1

Answer: (C), (D)

$P(E)=P$ (at least one of the dice shows up the face 5) $=1-P$ (none shows up the face five)
$=1-\frac{25}{36}=\frac{11}{36}$
Illy $P(F)=1-P$ (none of the dice shows up the face one)
$=1-\frac{25}{36}=\frac{11}{36}$
$E=\{15,25,35,45,55,65,51,52,53,54,56\}$
$F=\{11,12,13,14,15,16,21,31,41,51,61\}$
obviously $E$ and $F$ are neither mutually exceusively nor independent but they are equiprobable $\Rightarrow$ (C) and (D)