Probabality/Statistics

[kingcobra]

Can someone please help me with this problem?

A 3 card hand is dealt from a standard 52 card deck, and then one of the 3 cards is chosen at random.

1.) If the chosen card is a club, what is the probability that it is the only club in the hand?
2.) If the chosen card is a club, what is the probability that exactly two of the cards in the hand are clubs?
3.) If the chosen card is a club, what is the probability that all of the cards in the hand are clubs?
4.) If the chosen card is not a club, what is the probability that none of the cards in the hand is a club?

 

[HallsofIvy]

Can someone please help me with this problem?

A 3 card hand is dealt from a standard 52 card deck, and then one of the 3 cards is chosen at random.

1.) If the chosen card is a club, what is the probability that it is the only club in the hand?

So this is saying "if one card is a club, what is the probability the other two cards are not?" Suppose the first card dealt is a club. Now there are 51 cards left, 39 of them "non-clubs". What is the probability the second card drawn is NOT a club? Give that the second card is not a club, there are now 50 cards left, 38 of them "non-clubs". What is the probability the third card drawn is NOT a club? Multiply those together to get the probability of dealing "non-club, non-club" in that order. Do the same thing for "non-club, club, non-club": The probability the first card drawn is a non-club is 39/52, we assume the second card is a club so there are now 50 cards 38 of them are non-clubs: the probability the third card is not a club is \(\displaystyle \frac{39}{52}\frac{38}{50}. Similarly the probability the first two cards dealt you are non-clubs is \(\displaystyle \frac{39}{52}\frac{38}{51}. The probability of "two non-clubs given that one card is a club" is the sum of those three probabilty.

2.) If the chosen card is a club, what is the probability that exactly two of the cards in the hand are clubs?
3.) If the chosen card is a club, what is the probability that all of the cards in the hand are clubs?
4.) If the chosen card is not a club, what is the probability that none of the cards in the hand is a club?

Do the rest in the same way.\)\)

 

[kingcobra]

Probability/Statistics

Thank You Much