Answer to Question #239742 in Statistics and Probability for Dion Gray

Question

In all fours, 6 cards are dealt from a 52-card deck to each of 4 players and then

a card is dealt face up to determine the trump suit. The four players form two teams of two

players each. Suppose that a 10 of clubs is dealt as the face up card. Suppose also, that the

first player was dealt with a Jack and 3 cards with ranks less than 10, of the trump suit.

What is the probability that the second player dealt gets the highest trump in the deck i.e.

Ace of clubs?

Answer 1

There are a total of 52 cards, the first player got 6 cards, 10 of clubs is dealt as the face up card, out of it so 45 cards remain (52- 6-1= 45)

Clubs is the trump suite right now and the first player got 4 cards out of it so 8 of clubs remain.

So the probability to get a trump is 8/45= 0.1777

The probability to Ace of clubs = 1/8*0.1777=0.125*0.1777=0.0222125

Of 6 cards are dealt from deck to each players.

So the probability that the second player dealt gets the highest trump in the deck = 6*0.0222125= 0.133275