Question

PLEASE HELP> DUE TOMORROW

Use the fundamental principles of counting to find the number of outcomes for the situation of flipping a fair coin six times. can you find the probability that you will get heads all six times?

I started a chart but i hhave no idea what to do and my teacher doesnt explain

Answer 1

@sami-21

Answer 2

you have two choices for each toss, H and T

Answer 3

if you flip 6 times, the counting principle tells you there are
\[2\times2\times2\times2\times2\times2=2^6=64\] possible outcomes

Answer 4

i know the possible outcome is 64 but idk how to get the other number :/

Answer 5

that is, 64 possible combinations of heads and tails
there is only one way to get all heads

Answer 6

that would look like
H, H, H, H , H, H

Answer 7

so your answer is
\[\frac{1}{64}\]

Answer 8

but what about the other answers? idk how to get them

Answer 9

it would be harder if the question was "what is the probability you get 2 heads and 4 tails, but this one was easier because there is only one way to do it

Answer 10

what others? that is the only question i see posted

Answer 11

lol im so confused hold on ill attatch a picture of my chart i had to draw

Answer 12

this!

Answer 13

ah now that is a different question

Answer 14

whoops! can you tell my teacher hasnt taught me anything? its the first day of school too

Answer 15

you need all the numerators, each one of which is \(\dbinom{n}{k}\) here \(n=6\) and
\(k=0,1,2,3,4,5,6\)

Answer 16

idk why that was so spaced out

Answer 17

i am often spaced out
we can do this an easy way

Answer 18

so the n would fill out to be 6,12, and 18?

Answer 19

real easy
look at the 6th row of pascal's triangle and copy off the number for the numerator

Answer 20

no you compute like this
\[\dbinom{6}{1}=\dbinom{6}{5}=6\]
\[\dbinom{6}{2}=\dbinom{6}{4}=\frac{6\times 5}{2}=3\times 5=15\]
\[\dbinom{6}{3}=\frac{6\times 5\times 4}{\
3\times 2}=5\times 4=20\] those are your numerators

Answer 21

how did you decide to do the 6 ovver 1 6 over 5 6 over 2 and 6 over 4???

Answer 22

it is called "n choose k" and it is the number of ways to choose \(k\) items out of \(n\)
look at the 6th row of pascals triangle here
http://ptri1.tripod.com/
you will see the numbers
\[1,6,15,20,15,6,1\] and those are your numerators

Answer 23

if you have not seen this, i have no idea what you are supposed to do, unless they want you to write down all 64 possible combinations of heads and tails and count

Answer 24

haha yeah but thank you sooo much for helping me with the answer !! (: