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Question

A card is randomly drawn from a deck of 52 cards. What is the probability getting a five of Spade or Club?
Options:
A .  $MF#%\dfrac{1}{52}$MF#%
B .  $MF#%\dfrac{1}{13}$MF#%
C .  $MF#%\dfrac{1}{26}$MF#%
D .  $MF#%\dfrac{1}{12}$MF#%
Answer: Option C

Answer : Option C

Explanation :

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Solution 1
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Total number of cards, n(S) = 52
E = event of getting a five of Spade or Club
n(E) = 2 (∵ a five of Club, a five of Spade = 2 cards)

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

---------------------------------------------------------------------------------------- Solution 2 ----------------------------------------------------------------------------------------
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) = $MF#%\dfrac{1}{52}$MF#%


P(Club Cards of Number 5) = $MF#%\dfrac{1}{52}$MF#%

Here, clearly the events are , 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)

$MF#%= \dfrac{1}{52} + \dfrac{1}{52} = \dfrac{1}{26}$MF#%



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