Question

Calculate the probability of completing a straight if you have 4 cards that are in sequence. Do this both for the standard case of one deck of cards, or the casino case of an infinite supply of cards.

Answer 1

(A) Prob of getting straight (given scenario) = 0.166667

(B) Prob of getting straight (Casino scenario) = 0.153846

Explanation:

Probability of getting straight when standard deck of card

Since we 4 cards are already drawn, number of cards in the deck = 48

There are 8 possible cards in the deck to complete straight

Eg . if you have 4,5,6 & 7 then there are four 3’s and four 8’s in the deck that can complete straight.

Prob of getting straight (given scenario) = #of possible cards/# total number of remaining cards

= 8/48

=0.166667

Prob of getting straight (given scenario) = 0.166667

Probability of getting straight when casino case (infinite supply of cards)

Since we have infinite cards in supply, number of cards in the deck = 52

Number of cards in hand that doesn’t matter here.

There are still 8 possible cards in the deck to complete straight

Prob of getting straight (Casino scenario) = #of possible cards/# total number of remaining cards

= 8/52

=0.153846

Prob of getting straight (Casino scenario) = 0.153846