The question: Suppose that three cards are drawn from a deck of cards with replacement, what is the probability of getting one or more hearts?

I think of the question as asking P(one heart or two hearts or three hearts), then I find P(one heart) and P(two heart) and finally P(three hearts), then add them up.

Here's what I did:

P(one heart) = (13/52)*(39/52)*(39/52)*3 (because the heart can appear as the second card or the third)
P(two heart) = (13/52)*(13/52)*(39/52)*3 (similar reason)
P(three heart) = (13/52)^3 * 3 (similar reason)

and found ~0.61 chance of getting one or more hearts.

Is that correct? I'm just not sure about what I did.

Thank you!

I made a probability tree.

The tree came out to have 64 different suite combination, and only 37 of those combination had the correct suite.

The odds then were

37/64 or ~ 57.8 percent.

You can also use the "binomial probability" form.



Where

Where x is the number of successes we want, n is the number trials, p is the chance of success, and q is the chance of failure.

For this question we have

P(1)+P(2)+P(3) (Because we want the odds of 1 heart, 2 hearts, and 3 hearts)

x = 1.. 2... 3, n=3, p=0.25, q=0.75



simplified we have



And this also ends up being about 57.8 percent

There is only 1 way to have three hearts so you should not have multiplied by three in calculating P(three heart)!

Ok, my method:

P(no heart) = (39/52)^3

P(at least a heart) = 1 - (39/52)^3

Shorter, simpler! :)

Quote:

---

Originally Posted by kyva1929

P(three heart) = (13/52)^3 * 3 (similar reason)

---

My previous post was to point out the error in the above line of reasoning given in the original question, the * 3 part is incorrect as there is only one way to have three hearts. I did not mean that the question wanted a three of hearts. I used the same notation that kyva used.

Nhatkiem please consider re rating my post as it is not incorrect!

Quote:

---

Originally Posted by elscarta

My previous post was to point out the error in the above line of reasoning given in the original question, the * 3 part is incorrect as there is only one way to have three hearts. I did not mean that the question wanted a three of hearts. I used the same notation that kyva used.

Nhatkiem please consider re rating my post as it is not incorrect!

---

I see, sorry, you didn't quote what you were referring to, I thought you were talking about P(3) alone. Unfortunately it won't allow me to change the rating at this time.

However I will try to track of your post in the future for rating when I am allowed to rate for you again.