Are the events A=face-up card is a black jack and B=get a true “Blackjack” independent? Why?
Question by Rachel: Are the events A=face-up card is a black jack and B=get a true “Blackjack” independent? Why?
Best answer:
Answer by JackAce
Of course not. There is a strong correlation between the dealer showing a face card and him having a blackjack.
If you don’t know anything about the dealer’s up card, the probability that he is dealt a blackjack is 4.8%.
If the dealer has a face card showing, then there is more than a 1/13 chance that he has a blackjack (7.7%).
This means that having a face card will increase the dealer’s chances of having a blackjack by over 60%. If the events were independent, there would be no change in the frequency. Thus, they are NOT independent events.
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Tags: A=faceup, B=get, Black, Blackjack, Card, events, independent, Jack, True
August 8th, 2010 at 5:48 am
JackAce – you usually know what you’re talking about, so I’m not going to outright say “your wrong”. Still, I’m not so sure that’s what this guy is asking.
I think he’s actually asking about “BLACK” Jacks – as in the Jacks that are Clubs and the Jack of Spades.
Jacks that are actually black have NOTHING to do with getting a “Blackjack” in the game of Blackjack. A Blackjack is simply being dealt an Ace along with any Ten, Jack, Queen, or King. These 2 cards must be your first 2 cards – then you have a “Blackjack”.