If you flip two pennies ten times, how many times do you predict they will both land heads up why?

Question

If you flip two pennies ten times, how many times do you predict they will both land heads up why?

Answer 1

5 times because there is an equal chance for both heads and tails.

Answer 2

I would say it is 25% probability that both will land heads up.  Each penny has a 50% chance on each toss, so, on the predicted 5 tosses where one lands heads up, the other one has a 50% chance.  What that comes down to is 2 or 3 tmes out of 10 tosses they should both come up heads.

Don't expect it to work out that way every time, though.  Ten is a very small sample, and that makes any variability large.  To really test out the hypothesis, a sample of 100 tosses would be better.

Anthony, I think a couple of us were making the assumption that both pennies are being tossed together. Otherwise, how could you have both of them do anything on one toss?

Answer 3

@oikos:

How do you figure the probability is 1/4?

Prob. of penny A landing on heads: 1/2

Prob. of penny B landing on heads: 1/2

Prob. of them both landing on heads: 1/2, since they both have the same equal chance of landing on heads.

Now, this answer is assuming both pennies are started with the same side facing up.

Answer 4

How about 8 pennies instead.  If you flipped two pennies eight times they would come up heads 2 times, tails 2 times and 1 head and 1 tail 4 times.  It works like this.  If you flipped only one of the coins it would come up heads 4 times and tails 4 times.  For the 4 heads, flip the second coin 4 times.  The second coin will come up heads twice and tails twice.  Thus for the 4 times when one coin came up heads the other coin would come up heads twice.  The same thing happens for the 4 times that the coin came up tails.  All together you get (H/H) (H/H) (H/T) H/T) (T/T) (T/T) (T/H) (T/H)

Answer 5

Two or three. The probability is 1/4.

Edit: Interesting point, Anthony. You are assuming that the penny tosses are dependent, as if the pennies were cemented together. I am assuming that the tosses are independent and therefore the probability of two heads is the product of the probabilities for each of the coins, 1/2 squared. or 1/4.

Answer 6

With the usual idealized assumptions, the expectation of two heads in one toss is 1/4.  For ten tosses, the expectation value is simply ten times 1/4, or 25.

If a coin lands and stays on edge, you'll need to watch the movie to see what strange things happen.  But for the purposes of this test, simply discard the results of that toss.