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

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) φ (B)  1, 2  (C)  2, 4  (D)  1, 3

Tardigrade Admin · Accepted Answer

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 ∩ Q = φ

Q. 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

$ϕ$

${1, 2}$

${2, 4}$

${1, 3}$

Q. 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

ϕ

{1,2}

{2,4}

{1,3}

Q. 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

$ϕ$

${1, 2}$

${2, 4}$

${1, 3}$