Question

10. 300 9 от K LO A ci 2 of %D v

Problem 6: Now, find the following probabilities. Remember to ask yourself the questions,

• Is this a simple or compound probability?
• How many cards are being drawn?
• Which conjunction is used and should we add or multiply?
• If it is a compound probability, are the events dependent, independent, mutually exclusive, or not mutually exclusive?
• Which formula should be used?

Enter your answers as reduced fractions using / as the fraction bar.

1. What is the probability of drawing a king, replacing it, and then another king? P(KandK)=P(KandK)= Answer
2. What is the probability of drawing a black or a red card? AnswerP(R and B)P(R or B)P(B and R)P(B or R) = Answer
3. What is the probability of drawing a red queen, keeping it, and then drawing a black queen? (P((P( Answerblack queen and red queenred queen or black queenblack queen or red queenred queen and black queen )=)= Answer
4. What is the probability of drawing a king, keeping it, and then drawing another king? P(KP(K Answerorand K)=K)= Answer
5. What is the probability of drawing a heart? P(P( Answer)=)= Answer
6. What is the probability of drawing a face card (jack, queen, or king)? P(F)=P(F)= Answer
7. What is the probability of drawing an ace, a 2, and a 3, without replacement? P(AP(A Answerorand 22 Answerorand 3)=3)= Answer
8. What is the probability of drawing a Club or a 7? P(CP(C Answerorand 7)=7)= Answer
9. What is the probability of drawing an ace, a 2 or a 3? P(AP(A Answerorand 22 Answerandor 3)=3)= Answer

Answer 1

(i) P(K and K) = (4/52) * (4/52) = 16/2704 = 1/169.
(ii) P(R or B) = (26/52) + (26/52) = (1/2) + (1/2) = 1/1.
(iii) P(red queen and black queen) = (2/52) * (2/52) = 4/2704 = 1/676.
(iv) P(K and K) = (4/52) * (3/51) = 12/2652 = 1/221.
(v) P(heart) = 13/52 = 1/4.
(vi) P(drawing a face card) = 12/52 = 3/13.
(vii) P(an ace, a 2 and a 3) = (4/52) * (4/51) * (4/50) = 64/132600 = 8/16575.
(viii) P(a Club or 7) = (13 + 4 - 1)/52 = 16/52 = 4/13.
(ix) P(an ace, a 2 or a 3) = (4/52) + (4/52) + (4/52) = 12/52 = 3/13.