Question

Can someone plz help me with this probability problem!! :D Will give medal :)
2. Create a probability distribution table for the following experiment. A coin is tossed two times and after each toss a head or tails is recorded. Let the discrete random variable represent the number of heads in the two tosses.

Answer 1

a coin is tossed twice
there are \(2\times 2=4\) equally likely outcomes
not such a large number that we can't list them all \[\{HH, HT, TH, TT\}\]

Answer 2

what are the possible number of heads tossed?

Answer 3

4 times? :) but im not sure on how to graph it

Answer 4

whoa hold the phone

Answer 5

lets forget about a graph for a second

Answer 6

you got two coins, and not that it makes any difference, lets say the first is a dime, the second a nickel

Answer 7

you toss them both
do you understand what i meant by \[\{HH, HT, TH, TT\}\] is the set of possible outcomes ?

Answer 8

sorry the HH,HT,TH,TT confused me

Answer 9

ok so lets say the first coin is a dime, the second in a nickel
then \(HT\) means the dime was Heads and the nickel was Tails

Answer 10

is it more clear now?

Answer 11

nope im still confused :(

Answer 12

ok lets try with a picture

Answer 13

okay :)

Answer 14

do you understand that table?

Answer 15

yes :)

Answer 16

ok so now you see there are four possible equaly likely outcome right? i just abbreviated them as \[\{HH, HT, TH, TT\}\]

Answer 17

so then it would be 3/4 of the possible number of heads tossed or am i still wrong? :)

Answer 18

ok now we got all possible outcomes, now lets see what the possible number of heads are in two rolls

Answer 19

okay

Answer 20

start with \(HH\) how many heads?

Answer 21

1? :)

Answer 22

???

Answer 23

or is it 2? ._.

Answer 24

yes, 2

Answer 25

so one possibility is you get two heads
how about \(HT\)?

Answer 26

1 right?

Answer 27

right m

Answer 28

and \(TH\)?

Answer 29

1 as well?

Answer 30

yes
and finally \(TT\)

Answer 31

0 :)

Answer 32

yeah good
so if we have a random variable, usually denoted by \(X\) there are three possible values for \(X\) \[X=0,X=1,X=2\]

Answer 33

now for the distribution
\[X=0\] means you get no heads, i.e. two tails
how many ways are there to do that?

Answer 34

what do you mean how many are there to do that? :(

Answer 35

there are four possible outcomes , abbreviated as \[\{HH, HT, TH, TT\}\]
out of those, how many are TT (it is a silly question kind of, since the answer is obvious)

Answer 36

ah it would be 1 :)

Answer 37

right
and since there are four equally likely outcomes, \[P(X=0)=\frac{1}{4}\]

Answer 38

now how many ways can you get \[X=2\]

Answer 39

3 times right? :)

Answer 40

nope

Answer 41

how may tosses has two heads?

Answer 42

how many HH do you see in \[\{HH, HT, TH, TT\}\]

Answer 43

ohh ok i was thinking of the possible heads that i could get

Answer 44

it would also be 1

Answer 45

right so \[P(X=2)=\frac{1}{4}\]
and finally how many ways can \(X=1\)?

Answer 46

does that go for the TH?

Answer 47

2? :)

Answer 48

yes
so \[P(X=1)=\frac{2}{4}\] which you want to reduce to say \[P(X=1)=\frac{1}{2}\]

Answer 49

okay :)

Answer 50

now is it that i have to graph it? :)

Answer 51

how all we need to do is write the complete probability distribution which we already have \[P(X=0)=\frac{1}{4}, P(X=1)=\frac{1}{2}, P(x=2)=\frac{1}{4}\]

Answer 52

i don't know what the table is supposed to look like

Answer 53

you got an example?

Answer 54

yes wait a sec :)

Answer 55

sorry it wont submit is it ok if i draw it

Answer 56

sure