Question

A bridge hand consists of 13 randomly-dealt cards from a standard deck of 52 cards.

What is the probability that, in a randomly-dealt bridge hand, there is no card that is a ten or higher? (By ten or higher we mean that a card is either a ten, a jack, a queen, a king, or an ace.)

Answer 1

Note:- A standard deck of card contain 4 suits ( spades, hearts, dimond, clubs ) and each suits contain 13 cards ( ace, kings, queens, jacks, 10, 9, 8, 7, 6, 5, 4, 3, 2 ). That is a standard deck of card contain total 52 cards.

[ There are 4 suits and each suits contain the number of cards 10 or higher than ten is 5 (10, jack, queen, king, ace ) ]

So, number of cards which is equal to ten or higher than ten = 4×5 = 20

Number of cards which is lower than 10 is = 52-20 = 42.

Now, a bridge hand consists of 13 randomly-dealt cards from a standard deck of 52 cards are drawn, and we want to find the probability that there is no card that is a ten or higher than ten. This probability is equal to that there is all the card lower than ten.

A: event denoting that all the 13 cards are lower than ten.

By the classical definition of probability, our required probability is given by,

P(A) = ( total no of ways fro choosing 13 cards from 52 cards which is lower than ten / total no of ways for choosing any13 cards from 52 cards )

[ Using concept: 13 cards which is lower than ten are chosen from 32 cards in ways, and any 13 cards are chosen from a standard deck of cards which contain total 52 cards in ways.

And classical definition of probability:-

probability of an event = ( total no of favorable outcome of this event/size of sample space ) ]