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?

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 $\ge$ 7).

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

The probability can be calculated as follows:

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