A die is thrown and a card is selected ar random from a deck pf 5… - Vidyadip

MCQ

A die is thrown and a card is selected ar random from a deck pf $52$ playing cards. The probability of getting an even number of the die and a spade card is

A
$\frac{1}{2}$
B
$\frac{1}{4}$
✓
$\frac{1}{8}$
D
$\frac{3}{4}$

✓

Answer

Correct option: C.

$\frac{1}{8}$

A Sample space when a die is thrown,
$S_1 = \{1, 2, 3, 4, 5, 6\} \Rightarrow n(S_1) = 6$
Let A be the event that getting even number.
$A = \{2, 4, 6\} \Rightarrow n(A) = 3$
$\Rightarrow\ \text{P(A)}=\frac{3}{6}=\frac{1}{2}$
A card is selected from a deck of $52$ cards.
$\text{n}(\text{S}_2)= {^{52}}\text{C}_2=52$
Let $B$ be the event that getting spade card.
$\text{n(B)}= {^{13}}\text{C}_2=13\Rightarrow\ \text{P(B)}=\frac{13}{52}=\frac{1}{4}$
Required probability $= P(A) \times P(B)$
$=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$

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