# A card is drawn at random from a deck of 52 playing cards. Find the probability that it is a club or a king.

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A card is drawn at random from a deck of 52 playing cards. Find the probability that it is a club or a king.

1. 6/13
2. 4/13
3. 0
4. 7/15

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Correct Answer - Option 2 : 4/13

Concept:

A standard deck of playing cards contains 52 cards.

Divided equally into two colours "Red" and "Black".

Deck of 52 cards has four suits "Spades", "Hearts", "Diamonds" and "Clubs".

Hearts and Diamonds come in Red colour and Spades and Clubs comes in Black colour.

Every 4 suits contain 13 cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, Ace, Jack, Queen, King.

Calculation:

Let E = King and F = club

If E and F are events of the club and king, then the probability that one event or the other will occur denoted P(E or F), is given by

P(E or F) = P(E ∪  F) = P(E) + P(F) - P(E ∩ F)

$\rm P\left( {E{\rm{ }} ∪ {\rm{ }}F} \right) = {\rm{P}}\left( E \right) + {\rm{P(}}F) - {\rm{P}}\left( {E{\rm{ }} ∩ {\rm{ }}F} \right)$

$\frac{{13}}{{52}} + \frac{4}{{52}} - \frac{1}{{52}} = \frac{{16}}{{52}} = \frac{4}{{13}}$