Question

Thirteen cards are dealt onto the table from a standard deck of playing cards. What is the probability that there are mo...


Thirteen cards are dealt onto the table from a standard deck of playing cards. What is the probability that there are more red cards than black cards?

Answer

The standard deck of cards contains a total of 52 cards, in which, 26 cards are red and 26 cards are black.

 

In order to have more red cards than black cards, there should be at least 7 red cards among 13 cards.

Let X be the number of red cards out of 13 cards. So, the required probability that there are more red cards than black cards is given by  P(X  7).

 

Since the cards are picked without replacement, we use combinations (hypergeometric distribution) to find the probability.

The probability can be calculated as follows:

Statistics homework question answer, step 2, image 1

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