[1/26] A card is randomly drawn from a deck of 52 cards. What is the probability getting a five of Spade or

A card is randomly drawn from a deck of 52 cards. What is the probability getting a five of Spade or Club?

1/52

1/13

1/26

1/12

Explanation:

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Solution 1
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all number of cards, $n\left(S\right)$ = 52

E= event of getting a five of Spade or Club

$n\left(E\right)$ = 2[ a five of Club, a five of Spade = 2 cards]

$\text{P(E) = }\dfrac{\text{n(E)}}{\text{n(S)}} = \dfrac{2}{52} = \dfrac{1}{26}$

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Solution 2

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Total number of cards = 52

Total number of Spade Cards of Number 5 = 1

Total number of Club Cards of Number 5 = 1

P[Spade Cards of Number 5] = $\dfrac{1}{52}$

P[Club Cards of Number 5] = $\dfrac{1}{52}$

Here, clearly the events are mutually exclusive events.

By Addition Theorem of Probability, we have

P[Spade Cards of Number 5 or Club Cards of Number 5]

= P[Spade Cards of Number 5] + P[Club Cards of Number 5]

$= \dfrac{1}{52} + \dfrac{1}{52} = \dfrac{1}{26}$

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