Final answer:
To find the probability of being dealt a bridge hand with at least one heart, calculate the probability of a hand without hearts by using combinations and subtract from 1.
Step-by-step explanation:
To calculate the probability that a bridge hand is not void in any suit, first, we need to understand what this means. A hand void in a suit does not contain any cards from that suit. We need the probability of a hand that has at least one card from each suit, including at least one heart. Since the question only asks for hearts, we will focus on that.
There are 39 cards in the standard deck that are not hearts and 13 cards that are hearts. To deal a hand void of hearts, you would have to select all 13 cards from the 39 non-heart cards. The total number of ways to choose 13 cards from 39 is given by the combination formula C(39, 13).
The total number of possible bridge hands is the number of ways to choose 13 cards from the entire deck of 52 cards, which is given by C(52, 13).
Therefore, the probability of being dealt a hand not containing a heart is:
C(39, 13)
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C(52, 13)
This ratio gives the probability of selecting a hand that contains no hearts. Subtract this probability from 1 to find the probability of getting at least one heart in a 13-card hand.