Question 817507: Recall that there are 4 suits - spades, hearts, clubs, and diamonds - in a standard deck of playing cards. Suppose you play a game in which you draw a card, record the suit, replace it, shuffle, and repeat until you have observed 10 cards. Define X = number of hearts observed.
(a) Show that X is a binomial random variable.
(b) Find the probability of observing fewer than 4 hearts in this game.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Suppose you play a game in which you draw a card, record the suit, replace it, shuffle, and repeat until you have observed 10 cards. Define X = number of hearts observed.
(a) Show that X is a binomial random variable.
Binomial with n = 10; p(heart) = 13/52 = 1/4;
Draw results are independent because each drawn card is replaced.
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(b) Find the probability of observing fewer than 4 hearts in this game.
P(0<= x <=3) = binomcdf(10,1/4,3) = 0.7759
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Cheers,
Stan H.
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