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

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!

Update:

albert--no, different sides

Relevance

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.

• Login to reply the answers
• 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.

• Login to reply the answers
• Anonymous
• Login to reply the answers
• Login to reply the answers