2. Let A be the event that a person playing Texas hold\'um has hole cards that a

Question

2. Let A be the event that a person playing Texas hold'um has hole cards that are the same suit and B be that this player's hole cards forn will show that P(A) = 23.5% and P(B) = 5.8% , but take this as known for now. In a standard deck of cards, there is only one card of a particular suit with a particular value so that it is impossible to have hole cards that are both the same suit and a pair. What is a) b) The player's strategy is to only call before the flop if his hole cards form a pair or if they are c Given that this player told you that he has a pair, what is the probability that his two cards are d) Are A and B independent? the same suit. What is the probability that he will call before the flop? the same suit?

Explanation / Answer

a) as it is impossible to have hole cards that are both the same suit and pair ; therefore A and B are mutually exclusive

P(AnB )=0

b) Probability =P(AUB) =P(A)+P(B)-P(AnB) =0.235+0.058+0=0.293

c) here P(A|B) =P(AnB)/P(B) =0/0.058 =0

d) as for independence ; P(AnB) =P(A)*P(B)

but here P(AnB) =0 while P(A)*P(B) is not equal to 0/ therefore A and B are not independent.

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