Question

Two dice are thrown. The events $P$, $Q$ and $R$ are described as follows :
$P :$ getting an odd number on the first die.
$Q :$ getting an even number on the first die.
$R :$ getting atmost $6$ as sum of the numbers on two dice.
Then, the set of the event $P$ and $Q$ is

• A. $\phi$
• B. $\{1, 2\}$
• C. $\{2, 4\}$
• D. $\{1, 3\}$

Answer 1

Answer: (A)

Now,
$P =$ Getting an odd number on first die
$P = \{(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1)$,
$(3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (5, 1), (5, 2), (5, 3)$,
$(5,4), (5, 5), (5, 6)\}$
$Q =$ Getting an even number on the first die
$Q = \{(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1)$,
$(4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3)$,
$(6.4) , (6, 5), (6,6)\}$
Now, $P \cap Q = \phi$