Three cards are drawn successively with replacement from a well shuffled deck of 52 playing cards. If getting a card of spade is considered a success, find the probability distribution of the number of successes.
Text Solution
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Sol. Total cards = 52
Spade cards = 13
Probability of success p = 
= 
∴ q = 1 – p = 1 – 
= 
Let X be the number of success
∴ P(X = 0) = q 3 = 
= 
⇒ P(X = 1) = 3 q 2 P = 3 
= 
P(x = 2) = 3qp 2 = 3 
= 
⇒ P(X = 3) = P 3 = 
= 
∴ Required probability distribution is 
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