Question

Help please

Answer 1

with?

Answer 2

each time 2 outcomes are possible, namely head and tail

Answer 3

so 8 outcomes right?

Answer 4

yes!

Answer 5

so for part one, it would be 2*2*2*2=8?

Answer 6

now for part 2

Answer 7

please wait:
it is 2*2*2*2=16

Answer 8

yeah but isn't it a total of 8 outcomes

Answer 9

more precisely:
we have 2 possible outcomes for each flip, so when we multiply, we get:
\[\Large 2 \times 2 \times 2 \times 2 = 16\]
that number expresses the possible outcomes

Answer 10

if we add:
2+2+2+2 we get 8
nevertheless that number is not interesting for your exercise

Answer 11

okay so 2*2*2*2=16 :]

Answer 12

correct!
I'm sorry for my previous error

Answer 13

It is alright!

Answer 14

Let's move on to part II

Answer 15

ok!

Answer 16

here we have to do the subsequent reasoning:
lets suppose to start from a head (H)
then the next flip can be another head or a tail, so we have these outcomes:
\[\Large \begin{gathered}
HH \hfill \\
HT \hfill \\
\end{gathered} \]

Answer 17

Yes

Answer 18

whereas if we start from a tail (T), then next flip can be another tail or a head, so we get these other possible outcomes:
\[\Large \begin{gathered}
TH \hfill \\
TT \hfill \\
\end{gathered} \]

Answer 19

okay

Answer 20

in total we got these four outcomes:
\[\Large \begin{gathered}
1)HH \hfill \\
2)HT \hfill \\
3)TH \hfill \\
4)TT \hfill \\
\end{gathered} \]

Answer 21

So that is part II? HH,HT, TH, and TT

Answer 22

no, we have to finish :)

Answer 23

okay

Answer 24

next, let's start from the outcome 1)
then next flip can be a head or a tail, so we get these outcomes:
\[\Large \begin{gathered}
HHH \hfill \\
HHT \hfill \\
\end{gathered} \]

Answer 25

okay

Answer 26

now, let's start from outcome 2), then next flip can be a head ot a tail, so we get these new outcomes:
\[\Large \begin{gathered}
HTH \hfill \\
HTT \hfill \\
\end{gathered} \]

Answer 27

Yes, :} Would the next be, THH and THT

Answer 28

correct!

Answer 29

and I'm guessing the next is TTH and TTT

Answer 30

and the next two new outcomes are:
\[\Large \begin{gathered}
TTT \hfill \\
TTH \hfill \\
\end{gathered} \]
since I have started from outcome 4)

Answer 31

Does it matter what order?

Answer 32

no, the order of the outcomes, is not important
so, in total we got these outcomes:
\[\Large \begin{gathered}
a)HHH \hfill \\
b)HHT \hfill \\
c)HTH \hfill \\
d)HTT \hfill \\
e)THT \hfill \\
f)THH \hfill \\
g)TTT \hfill \\
h)TTH \hfill \\
\end{gathered} \]

Answer 33

Okay :}

Answer 34

now, we have to start from outcome a) and, with the same procedure we get these two new outcomes:
\[\Large \begin{gathered}
HHHH \hfill \\
HHHT \hfill \\
\end{gathered} \]

Answer 35

Yup :}

Answer 36

and then it would be HHTH and HHTT

Answer 37

starting from outcome b) I get these ones:
\[\Large \begin{gathered}
HHTH \hfill \\
HHTT \hfill \\
\end{gathered} \]

Answer 38

and we have to repeat the same procedure for the remaining outcomes c), d), e), f), g) and H)

Answer 39

so we get these outcomes:
\[\Large \begin{gathered}
1)HHHH \hfill \\
2)HHHT \hfill \\
3)HHTH \hfill \\
4)HHTT \hfill \\
5)HTHH \hfill \\
6)HTHT \hfill \\
7)HTTT \hfill \\
8)HTTH \hfill \\
9)THTT \hfill \\
10)THTH \hfill \\
11)THHT \hfill \\
12)THHH \hfill \\
13)TTTT \hfill \\
14)TTTH \hfill \\
15)TTHT \hfill \\
16)TTHH \hfill \\
\end{gathered} \]

Answer 40

that is the answer for part II

Answer 41

as you can see there are 16 possible outcomes, namely the number which we have computed in part I

Answer 42

Yes :}

Answer 43

now, for part III, we have highlight those outcomes which contains two T, namely TT

Answer 44

how many outcomes contain two (T)

Answer 45

2 or more or just two

Answer 46

I got six outcomes, precisely the subsequent outcomes:
#4, #6, #8 ,#10, #11, #16

Answer 47

Okay :}

Answer 48

so the probability to have two flips which comes up with (T) is:
p=favorable outcomes/possible outcomes=6/16
am I right?

Answer 49

Yes

Answer 50

But would't 6/16 be reduced

Answer 51

@Michele_Laino

Answer 52

it is:
\[\Large p = \frac{6}{{16}} = \frac{3}{8}\]

Answer 53

for part II right?

Answer 54

for part III is right!

Answer 55

oh okay part III?

Answer 56

next is part IV

Answer 57

ok!

Answer 58

here we have to highlight those outcomes which contain three (H).
How many outcomes do contain three (H) ?

Answer 59

Okay so #2, #3, #5, and #12

Answer 60

correct! we have 5 outcomes,
so the requested probability, is:
p=favorable outcomes/possible outcomes=\[\Large p = \frac{5}{{16}}\]

Answer 61

oops.. sorry we have 4 outcomes, so the requested probability is:
\[\Large p = \frac{4}{{16}} = \frac{1}{4}\]

Answer 62

okay :}

Answer 63

Thank you sooo much !!!!!!!

Answer 64

:) :)