Question

Suppose that a single card is drawn from the deck, its suit is recorded, and the card is returned and ten the deck is reshuffled . if this process is repeated four times , what is the probability that a spade card will be drawn at least once?

Answer 1

What is the probability of drawing a spade card in each draw?

Answer 2

A standard deck has 52 cards, of which 13 cards are spades. So what is the probability of drawing a spade?

Answer 3

@LCSmith6892 Are you there?

Answer 4

Yes I'm here. 1/4?

Answer 5

Since the probability is the same each time, you can use the binomial probability formula

Answer 6

I'm having trouble remembering how to do any of it, to be honest.

Answer 7

You need the formula for binomial probability

Answer 8

is that \[\left(\begin{matrix}n \\ k\end{matrix}\right) p ^{k}q ^{n-k}\]

Answer 9

Yes!

Answer 10

Can you give me a hint on how to enter the data? For some reason on my paper I had written P(A|b) as the formula.

Answer 11

That's an entirely different formula P(A|b), looks like conditional probability

p is the probability, q is just 1-p.

n is the number of trials, 4 in this case.

"At least once" is the same thing as: 1 minus the probability of exactly zero times - which means k is zero.

Find the probability using the formula, then subtract it from 1.

Answer 12

p is the probability that you found a few posts back

Answer 13

Thank you! This looks a lot more familiar now.

Answer 14

The probability of drawing a spade card is 1/4 on each of the 4 draws. The probability of not drawing a spade card on each of the 4 draws is 1 - 1/4 = 3/4.
Therefore the probability of not drawing a spade card after 4 draws is:
\[\large P(0\ spades\ after\ 4\ draws)=(\frac{3}{4})^{4}\]\
So the probability that a spade card will be drawn at least once is given by:
\[\large P(1\ or\ more\ spade\ cards)=1-(\frac{3}{4})^{4}\]

Answer 15

That is very helpful, Kropot72! Thank you both so much.

Answer 16

You're welcome :)