If 5 coins are tossed simultaneously, what is the probability that at least one coin comes up heads

A. about 0.03
B. about 0.33
C. about 0.67
D. about 0.97

please explain your answer. thank you.

1 - .5^5 = 0.96875
D) about .97

at least one coin comes up heads means that:
1 coin or
2 coins or
3 coins or
4 coins or
all 5 coins are heads.

everything except all tails

the probability of flipping 5 tails is .5^5

1 - .5^5 ≈ .97

The answer is D. about 0.97.

There are two possible outcomes of a coin toss, so the number of possibilities is two to the power of something.

Given that there are five coins being tossed at the same time, the number of possibilities is...

2^5 = 32

In only one of the 32 possible outcomes is there no coin heads-up: that is the outcome in which all five coins land tails-up.

Thus the probability of at least one coin coming up heads is represented by...

P(at least 1 heads) = 1 - P(no heads) = 1 - 1/32 = 1 - 0.03125 = 0.96875 ~ 0.97

of coins come up heads in one trial: 0, 1, 2, 3, 4, 5

At least one coin comes up heads include 1, 2, 3, 4, 5
The complement of this event is 0 heads - 0

The probability of an event is equal to 1 minus the probability of its complement.
In mathematical terms: P(E) = 1 - P(E')

So P(at least one head) = 1 - P(no head) = 1 - P(all tails) = 1 - (1/2)^5 = 31/32
The answer is D.

You have 5 coins, you need at least one - i.e. one or more to come up as heads.

Draw a tree diagram,you should get something like this on most of your branches:

H->T->H->H->T

First coin heads, then tails, heads, head tails. If you draw all the branches you should have a total of 32 branches (2^5 - 2 because there are two options, 5 because there are five repetitions of these two options) you can now count all the branches of your tree diagram that DO NOT have one or more heads in them. Only one should have no heads: T->T->T->T->T So 31/32 have a head or more in them.