Question

The probability of obtaining the sequence {H, T, T, H, H} when you toss a fair coin 5 times equals

A. 1/32
B. 1/5
C. 1/2
D. 1/10

I think C but then again I suck at this..

Answer 1

they want exactly that sequence {H, T, T, H, H}
so {T, H, T, H, H} is not valid

Answer 2

This is the problem I'm having it doesn't say whether the order is important in this case or not

Answer 3

neigher is {H, H, T, T, H}

Answer 4

surely they want us to recognize the notation.

Answer 5

So you think it has to be in that exact order?

Answer 6

do you know what it means when they use curved brackets?

Answer 7

>So you think it has to be in that exact order?
it sounds like it,
I do not know the notation

Answer 8

it is \((\frac{1}{2})^5\)

Answer 9

but a sequence.......well what else than an exact sequence should it be?

Answer 10

or if you prefer
\[\frac{1}{2^5}\]

Answer 11

you flip a coin 5 times, there are \(2^5=32\) equally likely elements in the sample space
any particular sequence of head and tails has probability \(\frac{1}{32}\)

Answer 12

@torontoXO the magic here is that the idiots give the exact sequence

so it doesn't even matter how often you get a head or tail. they are only interested in their exact sequence.
and of all the coins you can throw, there's just that one that gives everything like they have specified. that's one out of all possibilities.

Answer 13

just one trail of events*

Answer 14

basically if they said you need
T-T-H

then out of
T-T-T
T-T-H
T-H-T
T-H-H
H-T-T
H-T-H
H-H-T
H-H-H

there's only one that is like they want.
in your case you throw more often, so more possibilities how it can go.

Answer 15

Ok so I think I get it. If it has to be in the exact order it only matters how often you could get the sequence or something like that?

Answer 16

yes exactly

you get the sequence, statistically, once with all the other possibilities
if you want the highly specified then statistically
you also get one of all the other with it.

Answer 17

so if you throw coins like that 32 times, you have a chance of 1.0 to have the exact sequence in it. and if you only throw one time, well it's just 1/32 chance to get that one out of the 32.

Answer 18

Ahhhhhhhh ok thanks a lot man hella appreciation