Question

A fair coin is flipped four times. What is the probability of getting heads at least once?

Answer 1

didn't we just do this?

Answer 2

no

Answer 3

oh you are right, 4 times. sorry

Answer 4

we can list them or we can use a formula. your choice

Answer 5

a formula

Answer 6

at least once means 1 or 2 or 3 or 4, so not 0
the probability you get zero heads is
\[(\frac{1}{2})^4\]so the probability you get at least one head is
\[1-(\frac{1}{2})^4\]

Answer 7

The sample space of the experiment is

hhhh
hhht
hhtt
httt
hhth
hthh
htth
htht

thhh
tthh
ttth
thth
thht
tttt
thtt
ttth

so the number of times of getting heads at least once is 15 out of 16.

But there is a better way.

If you know that the probability of getting a heads at least once is mutually exclusive of getting all tails then P[heads at least once] = 1 - P[all tails] = 1 - 1/16 = 15/16

Answer 8

of course zero heads mean all tails, i.e. you got
t t t t

Answer 9

satellite u r brainy