Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the 1st card is an ace, or the 2nd a two, o

Question

3 years ago

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Cards from an ordinary deck of 52 playing cards are turned face up one at a time. If the 1st card is an ace, or the 2nd a two, o

r the 3rd a three, or . . . , or the 13th a king, or the 14th an ace, or the 15th a two, and so on, we say that a match occurs. Compute the expected number of matches that occur.

Mathematics

1 answer:

Evgesh-ka [11] · Answer 1 · 2022-04-19T01:34:48+03:00

Answer:

Expected number of matches that occur = 4 matches

Step-by-step explanation:

First of all, let X_i be the event that when we turn over card i if it matches the required cards face.

Thus, for example X_1 is the event that turning over one card results in an ace while X_2 is the event that turning over second card reveals a deuce.

The number of matched cards "N" is given by the sum of this indicator random variable as shown in the attached file;