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  • Suppose you have two standard decks of playing cards, each containing 52 cards. If you draw a card at random from one deck and then draw another card at random from the second deck, what is the pro

Suppose you have two standard decks of playing cards, each containing 52 cards. If you draw a card at random from one deck and then draw another card at random from the second deck, what is the probability that both cards will be aces?

Option: 1

\frac{1}{256}


Option: 2

\frac{1}{169}


Option: 3

\frac{1}{221}


Option: 4

\frac{1}{676}


Answers (1)

best_answer

To find the probability of drawing two aces, we need to multiply the probability of drawing an ace from the first deck by the probability of drawing an ace from the second deck since the two events are independent.

The probability of drawing an ace from a standard deck of 52 cards is  \frac{4}{52} \text{ or } \frac{1}{13} since \frac{1}{256}  there are four aces in each deck. 

Since we are drawing one card from each deck, the events are independent, which means that the probability of drawing an ace from the second deck is also \frac{1}{13}.

Let E be the event of drawing two aces.

Therefore, the probability of drawing two aces is:

\\{P(E)=\frac{1}{13}\times \frac{1}{13}}\\ \Rightarrow P(E)=\frac{1}{169} \

So, the probability that both cards drawn will be aces is \frac{1}{169}.


 

Posted by

Gautam harsolia

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