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Probability — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsProbability1 Mark
Question
Choose the correct answer from the given four options.
A die is thrown and a card is selected at random from a deck of 52 playing cards. The probability of getting an even number on 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:

Let E1 = Event for getting an even number on the die

And E2 = Event that a spade card is selected.

$\therefore\text{P}(\text{E}_1)=\frac{3}{6}=\frac{1}{2}$ and $\text{P}(\text{E}_2)=\frac{13}{52}=\frac{1}{4}$

Then, $\text{P}(\text{E}_1\cap\text{E}_2)=\text{P}(\text{E}_1)\cdot\text{P}(\text{E}_2)$

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

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