Question

A card is drawn at random from a well shuffled standard deck of 52 cards. What is the probability of getting either a heart or a diamond?
1. \(\frac{{7}}{{16}}\)
2. \(\frac{{1}}{{2}}\)
3. \(\frac{{3}}{{13}}\)
4. \(\frac{{1}}{{4}}\)

Answer 1

Correct Answer - Option 2 : \(\frac{{1}}{{2}}\)

Given:

In the deck there are total 52 cards

Concept Used:

Probality = Nuber of possible cases/Number of total cases

If a deck of 52 cards there are 13 heart and 13 diamond cards

Calculation:

Total number of cards of heart and diamond is (13 + 13) = 26

Either a heart or a diamond can be get from this 26 cards in ²⁶C₁ = 26 ways

From total 52 cards 1 card can be drawn in ⁵²C₁ = 52 ways

Required probability = 26/52 = 1/2

∴ The probability of getting either a heart or a diamond is 1/2.