A game of draw poker deals five cards. You play a 100 hands of consecutive draws

Question

A game of draw poker deals five cards.

You play a 100 hands of consecutive draws that deals from a shuffled 52-card deck.

At the beginning of play you focus on counting your hands without Aces to determine if the dealer is fair or not.

There is a random chance of 0.659 that any one hand will not have an Ace.

You have counted 74 hands without an Ace in your 100 hands of play.

Do you have doubts the dealer is being fair?

Use continuity correction for calculation and state your level of doubt (Class 13 uses < 10% as a little suspicious, < 5% as suspicious, and < 1% as extremely doubtful).

Explanation / Answer

here expected number of hands without ace =np =100*0.659 =65.9

and std deviaiton =(np(1-p))1/2 =(100*0.659*(1-0.659))1/2 =4.74

threfore from normal approximation:

probability of having 74 or more number of hands without an Ace =P(X>=74) =1-P(X<=73)

=1-P(Z<(73.5-65.9)/4.74)=1-P(Z<1.6032) =1-0.9456 =0.0544

as probability is less than 10% and greater than 5%

therefore it falls under category  as a little suspicious

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