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The probability of getting heads on a single coin flip is 1 2 . The probability of getting nothing but heads on a series
Question
The probability of getting heads on a single coin flip is
1
2
. The probability of getting nothing but heads on a series of coin flips decreases by
1
2
for each additional coin flip. Enter an exponential function for the probability p(n) of getting all heads in a series of n coin flips. Give your answer in the form a(b)n. In the event that a = 1, give your answer in the form (b)n.
The equation is p(n) = .
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Mathematics
3 years
2021-08-29T05:14:13+00:00
2021-08-29T05:14:13+00:00 1 Answers
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Answers ( )
Answer:
I hope this helps 😀
Step-by-step explanation:
4
It can be done a lot easier: instead of calculating the probability of one head, two heads, three heads, … one just needs to calculate the probability of no heads: that is simply 0.5
0.5
n
. If you subtract it from 1, you get the probability you want: it’s because that’s the chance of not no heads, meaning at least one head. So, the formula is: 1−0.5
1
−
0.5
n
More formally: if X is throwing at least one head,
()=1−(¬)
P
(
X
)
=
1
−
P
(
¬
X
)
, where ¬
¬
X
is throwing zero heads.