A card is dealt from a full deck (no jokers). (a) Find the probability of being dealt a jack. (Enter your answer as a fraction.) (b) Find the probability of being dealt a jack given that you were dealt a card above a 6 (count aces high). (Enter your answer as a fraction.)   (c) Are the events "being dealt a jack" and "being dealt a card above a 6" independent? Why? Yes, being dealt higher cards does not change the probability of getting a jack. No, being dealt higher cards increases the probability of getting a jack.

Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter14: Counting And Probability
Section14.CR: Chapter Review
Problem 35E
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A card is dealt from a full deck (no jokers).

(a) Find the probability of being dealt a jack. (Enter your answer as a fraction.)


(b) Find the probability of being dealt a jack given that you were dealt a card above a 6 (count aces high). (Enter your answer as a fraction.)
 

(c) Are the events "being dealt a jack" and "being dealt a card above a 6" independent? Why?
  • Yes, being dealt higher cards does not change the probability of getting a jack.
  • No, being dealt higher cards increases the probability of getting a jack.    

(d) Are the events "being dealt a jack" and "being dealt a card above a 6" mutually exclusive? Why?
  • Yes, a jack is never above a 6.
  • No, a jack is above a 6.    

(e) Interpret the results of parts (c) and (d).
  • Dependent events are never mutually exclusive.
  • Independent events are never mutually exclusive.    
  • Dependent events are always mutually exclusive.
  • Dependent events are not necessarily mutually exclusive.
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