If you toss a coin, the probability of gettig heads is 1/2. If you toss a coin 2 times. the probability of getting heds each time is 1/2*1/2 or (1/2)^2.
-Write an expression to represent the probability of tossing a coin 'n' times and getting 'n' heads.
-Express your answer to the question above as a power of 2.
At first I thought the expression was (1/2)^n but then when I look at it again, it seems wrong.
It is right!!
Oh okay. Then for the second problem, would it be (1/2)^2?
I am sorry, but the second part of the problem "express your answer to the question as power of 2" is confusing to me. Certainly, if you flip the coin TWICE, then it's a power of 2, as you said, but if you flip it N times, I don't know you can express this as a power of 2.
they mean that n= n number of times in the equations
(1/2)^n
but the product is not corresct if u replce an exponent of 2 for the n...
the answer is said to be 2^-n
Oh...ok, of course...
2^-n is the same as (1/2)^n.
To represent the probability of tossing a coin 'n' times and getting 'n' heads, you need to multiply the probability of getting heads on each individual toss. Since the probability of getting heads on a single coin toss is 1/2, the expression for 'n' coin tosses and 'n' heads would be:
(1/2) × (1/2) × (1/2) × ... (n times)
In general, this expression can be written as:
(1/2)^n
So, your initial intuition is correct. The expression representing the probability of tossing a coin 'n' times and getting 'n' heads is indeed (1/2)^n.