Question

A fair coin is tossed 5 times.

(a) Find the probability that exactly 3 heads appear.
(b) Find the probability that no heads appear.

Answer 1

binomial probability i think

Answer 2

the sample space contains 2^5 outcomes

Answer 3

the binomial expansion for "5 times" is:

1 5 10 10 5 1, to with we use these as numerators and 2^5 as a denominator

Answer 4

#heads, prob

0, 1/2^5
1, 5/2^5
2,10/2^5
3,10/2^5
4, 5/2^5
5, 1/2^5

if i recall it right

Answer 5

so the probability of exactly three heads appearing is 10/2^5?

Answer 6

i believe so; might wanna turn that into a decimal with 4 places to it

Answer 7

.3125 is the answer?

Answer 8

and then 32 is the answer to no heads appearing?

Answer 9

i mean .03125

Answer 10

for the no heads

Answer 11

as long as I am remembering it right, id say yes

Answer 12

yes that was exactly correct! thank you so much!!!

Answer 13

@amistre64 : you are correct

Answer 14

youse welcome :)

Answer 15

yay!!

Answer 16

can you tell me why i would divide by ten to get the prpbability of 3 heads?

Answer 17

lol .... that would be "theory", not my department :)

Answer 18

hahah so you just knew to divide by 10?

Answer 19

what are you mean...dividing by 10?

Answer 20

it has something to do with nCr p^r (1-p)^r ; or some sort of quagmire

Answer 21

ooooooh okay gotcha!!!!

Answer 22

\[_{n}C_{r}p^r(1-p)^{n-r}\]

Answer 23

yeah, that one ;)