Question
A card is randomly drawn from a deck of 52 cards. What is the probability getting either a King or a Diamond?
A card is randomly drawn from a deck of 52 cards. What is the probability getting either a King or a Diamond?
Answer: Option A
, we have
P(King or a Diamond) = P(King) + P(Diamond) – P(King and Diamond)
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Answer : Option A
Explanation :
Total number of cards = 52
Total Number of King Cards = 4
$MF#%\text{P(King) = }\dfrac{4}{52}$MF#%
Total Number of Diamond Cards = 13$MF#%\text{P(Diamond) = }\dfrac{13}{52}$MF#%
Total Number of Cards which are both King and Diamond = 1$MF#%\text{P(King and Diamond) = }\dfrac{1}{52}$MF#%
Here a card can be both a Diamond card and a King. Hence these are not mutually exclusive events., we have
P(King or a Diamond) = P(King) + P(Diamond) – P(King and Diamond)
$MF#%= \dfrac{4}{52} + \dfrac{13}{52} – \dfrac{1}{52} = \dfrac{16}{52} = \dfrac{4}{13}$MF#%
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