Question

In an experimental performance of a single throw of a pair of unbiased normal dice, three events $E_1,E_2$ $\&E_3$ are defined as follows:
$E_1:$ getting a prime numbered face on each dice
$E_2$ : getting the same number on each dice
$E_3$ : getting a sum on two dice equal to 8 . Then:

• A. the events $E_1,E_2$ & $E_3$ are not mutually exclusive
• B. the events $E_1,E_2\&E_3$ are not pairwise mutually exclusive
• C. $P\left(E_3\mid E_1\right)-2/9$.
• D. All of these

Answer 1

Answer: (D)

$E_1=\{(2,2),(2,3),(2,5),(3,2),(3,3),(3,5),(5,2),(5,3),(5,5)\}$
$E_2=\{(1,1),(2,2),(3,3),(4,4),(5,5),(6,6)\}$
$E_3=\{(2,6),(3,5),(4,4),(5,3),(6,2)\}$
clearly $(1),(2)$ and $(3)$ are correct.