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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
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
  1. $\frac{1}{2}$
  2. $\frac{1}{4}$
  3. $\frac{1}{8}$
  4. $\frac{3}{4}$
✓

Answer

  1. $\frac{1}{8}$

Solution:

A Sample space when a die is thrown,

S1 = {1, 2, 3, 4, 5, 6} ⇒ n(S1) = 6

Let A be the event that getting even number.

A = {2, 4, 6} ⇒ 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) × P(B)

$=\frac{1}{2}\times\frac{1}{4}=\frac{1}{8}$

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