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24. You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that both cards are black. Express your answer as a simplified fraction.

25. You are dealt two cards successively (without replacement) from a shuffled deck of 52 playing cards. Find the probability that the first card is a King and the second card is a queen. Express your answer as a simplified fraction.

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Priyanshu Patel
Priyanshu PatelLv10
8 Mar 2021
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

Consider the experiment of selecting a playing card from a deck of 52 playing cards. Each card corresponds to a sample point with a probability.

(a) List the sample points in the event an ace is selected.

(b) List the sample points in the event a club is selected.

(c) List the sample points in the event a face card (jack, queen, or king) is selected.

(d) Find the probabilities associated with each of the events in parts (a), (b) and (c).

A deck of n cards numbered 1 through n is thoroughly shuffled so that all possible n! orderings can be assumed to be equally likely. Suppose you are to make n guesses sequentially, where the ith one is a guess of the card in position i. Let N denote ht number of correct guesses. (a) If you are not given any information about your earlier guesses show that, for any strategy, E[N]=1. (b) Suppose that after each guess you are shown the card that was in the position  in question. What do you think is the best strategy? Show that, under this strategy.

 

(c) Suppose that you are told after each guess whether you are right or or wrong. In this case, it can be shown that the strategy which maximizes  E[N] is one that keeps on guessing the same card until you are told you are correct and then changes to a new card. For this strategy, show that 

 

Hint: For all parts, express N as the sum of indicator Hint: For all parts, express N as the sum of the indicator.

 

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