help with an SAT math problem...please look?

Question

a coin with two faces is tossed three times. what is the possibility that the coin will land with the same face up all three times?

thanks!

albert--no, different sides

Answer 1

The probability of a coin landing heads or tails on any particular throw is 1/2. For the first throw, you don't care which result you get; so the odds of getting the "right" one are 2/2 (= 1 or unity). For the second throw, you have to match the first throw, so your odds are 1/2; likewise for the third throw. The probability of the series then is 2/2 * 1/2 * 1/2 or 2/8 = 1/4 or 25%.

You can figure this out another way by listing the possibilities for three throws of the coin:
hhh
hht
hth
htt
thh
tht
tth
ttt

There are eight possibilities, only two of which are three-of-a-kind; so the chances again are 2/8 = 1/4 or 25%.

Hope it helps.

Answer 2

Tim P. is incorrect. The prob. of heads all three times is 1/2*1/2*1/2 = 1/8. The same is true for tails all three times. I get the 1/2 because the prob of a tail is 1 out of 2. Same for a head.

Another way to see the answer is list the possibilities.

hhh
hht
hth
thh
htt
tht
tth
ttt

Notice that hhh comes up 1 out of the 8 possibilities and so does ttt.

Answer 3

Is it the same face on both sides?

Answer 4

.5x.5x.5
1/8 or 12.5%