# Thread: What is the probability of not drawing a club from a deck of cards

1. ## What is the probability of not drawing a club from a deck of cards

Hi,
Can someone help me with this please?

You draw 40 playing cards, 1 at a time, with replacement from a standard deck.
What is the probability of NOT drawing a club in 12 successive picks!

Thankyou!

2. ## Re: What is the probability of not drawing a club from a deck of cards

I don’t fully understand the question: “draw 40 playing cards” seems to contradict “12 successive picks.”

Since it’s with replacement, the deck remains intact for each draw. In a standard deck of 52 cards with Jokers excluded, there are 13 Clubs and 39 non-Clubs. Thus, the probability of not drawing a Club (i.e., drawing a non-Club) on any single draw is 39/52 = ¾.

For successive draws, the probability of not drawing a Club is compounded because each draw is independent: .

3. ## Re: What is the probability of not drawing a club from a deck of cards

Originally Posted by Con-Tester
I don’t fully understand the question: “draw 40 playing cards” seems to contradict “12 successive picks.”

Since it’s with replacement, the deck remains intact for each draw. In a standard deck of 52 cards with Jokers excluded, there are 13 Clubs and 39 non-Clubs. Thus, the probability of not drawing a Club (i.e., drawing a non-Club) on any single draw is 39/52 = ¾.

For successive draws, the probability of not drawing a Club is compounded because each draw is independent: .
Hi,
Sorry for not being clear enough!

In total you draw 40 cards 1 at a time and replace it before drawing the next card.
What I want to know is the probability of not drawing 12 clubs on the trot, at any time during the 40 picks

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