Geometric distribution. Johnny has 1,176 Pok´emon cards in total. Pok´emon EX is a special type...

sestigtalill

sestigtalill

Answered

2022-12-19

Geometric distribution. Johnny has 1,176 Pok´emon cards in total. Pok´emon EX is a special type of card, and Johhny has 39 EX-type cards. He is looking for an EX-type card, but all of the cards are completely mixed up and stored in a shoe box. His mother is calling him for dinner. What is the probability that Johnny will have to look through no more than 25 cards before he finds an EX-type card?

Answer & Explanation

Agour2q9

Agour2q9

Expert

2022-12-20Added 1 answers

Distribution: For  x = x  these must be a run of  ( x 1 )  failure followed by a success, so P ( x = x ) = θ ( 1 θ ) x 1 x = 1 , 2 , 3 , . . . ( 0 < θ < 1 ) I knows way of the geometric distribution let x be the numbers of failure's between the first success than P ( x = x ) = θ ( 1 θ ) x x = 0 , 1 , 2 , 3 , . . . P ( x 25 ) = P ( x = 0 ) + P ( x = 1 ) + + P ( x = 24 ) + P ( x = 25 ) = θ ( 1 θ ) 0 + θ ( 1 θ ) 1 + ( 1 θ ) 2 + + θ ( 1 θ ) 25 = θ [ 1 + ( 1 θ ) + ( 1 θ ) 2 + + ( 1 θ ) 25 ] = θ [ 1 ( 1 θ ) 26 ] [ 1 ( 1 θ ) ] = θ θ [ 1 ( 1 θ ) 26 ] = 1 ( 1 θ ) 26 where  θ = 39 1176 P ( x 25 ) = 1 [ 1 39 1176 ] 26 1 39 1176 26 = 0.5839

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