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Two cards from 52 card sets were missing. A card from the rest of the cards was selected randomly. What is the probability that it is a spade?


I have solved this problem like this,

enter image description here

So total → $\dfrac{36}{50}$

but the answer given is like→

enter image description here

Are they correct? And why can't I solve it in the way which I have done?

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    $\begingroup$ Does it make sense to you that removing two cards would increase the chance of getting a spade ? $\endgroup$ Dec 27, 2019 at 11:07

2 Answers 2

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They are indeed correct. You only calculated conditional probabilities. There remains to apply the formula of total probabilities which the recall (adapted to this case) in the first line of the image.

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The two cards missing can be anything, thus it doesn't affect the probability to get a spade, which is still $\frac{1}{4}$. Imagine all but one card was missing, i.e. 51 cards missing, the remaining one has the same probability to be a spade, that if you would select one card among the full set of 52 cards.

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