Question

Suppose that you toss a coin and roll a die. Attached is the sample space is shown in the figure below.What is the probability of obtaining tails or a four? (Enter the probability as a fraction.)

Answer 1

how many ways are there to get tails

Answer 2

6 right

Answer 3

yes, how many ways are there to roll a four

Answer 4

6? so it should be 1/6

Answer 5

6 ways to roll a four?

Answer 6

oh no only 1 way to roll a four

Answer 7

so how many ways total are there to either roll a 4 or get tails?

Answer 8

7?

Answer 9

good, out of how many ways total

Answer 10

7/12 is the probability

Answer 11

totally over thinking that problem

Answer 12

yep, the answer is 7/12

Answer 13

thanks for your help!

Answer 14

you're welcome

Answer 15

can you possibly help with another problem?

Answer 16

sure

Answer 17

The Emory Harrison family of Tennessee had 13 boys. What is the probability of a 13-child family having 13 boys? (Assume that the probability of having a boy or a girl is the same. Round your answer to six decimal places.)

Answer 18

because we have nothing but boys, we would get this

(1/2)^n = (1/2)^(13) = (1^13)/(2^13) = 1/8192

again this only works because we're picking the same option each time (in this case, boys)

Answer 19

what is that formula?

Answer 20

the formula is (1/2)^n where n is the number of boys

Answer 21

ok im following

Answer 22

well all I did was plug in n = 13 and simplified to get 1/8192 (it's shown above)

Answer 23

i gotya. its really pretty simple when you break it down. just got to know the formula lol

Answer 24

yes keep in mind that it only works if you have nothing but one gender

Answer 25

right if you had two gender you would do (1/2)^n +(1/2)^g.. where n is equal to number of boys and g is equal to number of girls?

Answer 26

not quite

Answer 27

it's a bit more complicated if you have both genders involved

Answer 28

ok ill leave that alone for now then lol

Answer 29

if you're curious, look up the binomial distribution and you'll find more info about it

Answer 30

absolutely! u must be a teacher lol

Answer 31

kinda, I'm a student learning to become one

Answer 32

i got one last probability problem if your willing to help

Answer 33

sure go for it

Answer 34

well your gonna make a great teacher.

Answer 35

thanks

Answer 36

What is the probability of obtaining exactly four tails in five flips of a coin, given that at least three are tails? (Enter the probability as a fraction.)

Answer 37

the key thing to notice is that it says "given that at least three are tails"

Answer 38

so if we have 5 flips, then the following is possible

a) 3 tails, 2 heads

b) 4 tails, 1 head

c) 5 tails, 0 heads

Answer 39

we have to list out all the possible cases for each scenario

Answer 40

ok im following

Answer 41

i thought the probability would just be 1/2 because it can only be heads or tails

Answer 42

one sec

Answer 43

ok

Answer 44

are you familiar with permutations and combinations?

Answer 45

yes sir

Answer 46

so if ordered mattered, then how many ways are there to arrange 5 items

Answer 47

5! which is 5*4*3*2*1=120

Answer 48

good so if you are arranging TTTHH, then you'll have duplicates

to remove the duplicates, you divide by 3!*2! = 6*2 = 12

so

120/12 = 10

Answer 49

this means that there are 10 ways to arrange TTTHH and they are listed below

TTTHH
TTHTH
TTHHT
THTTH
THTHT
THHTT
HTTTH
HTTHT
HTHTT
HHTTT

Answer 50

this takes care of scenario a) where we have 3 tails and 2 heads

Answer 51

correct

Answer 52

for scenario b) we have these cases

TTTTH
TTTHT
TTHTT
THTTT
HTTTT

there are 5 cases above and they are easily countable (so no need for a formula here)

Answer 53

and finally in scenario c) we have just this one case: TTTTT

Answer 54

in total, there are 10+5+1 = 16 possible outcomes

Answer 55

so it would be 1/16?

Answer 56

The original question was

What is the probability of obtaining exactly four tails in five flips of a coin, given that at least three are tails? (Enter the probability as a fraction.)

Answer 57

there are 16 ways to get at least 3 tails

there are 5 ways to get what you want (exactly 4 tails, look at scenario b above)

so the probability is 5/16

Answer 58

ahhhhhh. i understand now. you make it seem so simple

Answer 59

that's great, i'm glad you do

Answer 60

thank you for all your help!

Answer 61

you're welcome