Question

Probability of Rain on a Day=0.2
What is the probability of raining atleast 2 days in a week ?

Answer 1

there are 2 ways to approach this

Answer 2

out of 7 days in a week, it would be easier to calculate the compliment statement of:

P(rain at most 1 day out of 7)

Answer 3

P(0) + P(1)

Answer 4

... or is the compliment; does not rain at most 1 day out of the week?

Answer 5

P(0) + P(1)
at most 1 day of rain


P(2) + P(3) + P(4) + P(5) + P(6) + P(7)
at least 2 days of rain


in any case .... the long way is:
\[\sum_{2}^{7}~\binom{7}{r}~.2^r~.8^{7-r}\]

Answer 6

@amistre64 how do we solve the equation ?

Answer 7

im thinking the 1 - P0+P1 is quicker "by hand"\[1-\binom{7}{0}~.2^0.8^7-\binom{7}{1}~.2^1.8^6\]

Answer 8

Actually I don't know summation and other things could you give it to me in a simple version @amistre64

Answer 9

the (7 0) is just another way to write 7 "choose" 0, by this time you should have already gone thru the permuatation and combination material

7 C 0 is a common notation, but some texts use C(7,0)

does any of that look familiar?

Answer 10

No,nothing looks familiar to me.Could you write the equation in a multiplication/addition/division/subtraction format @amistre64

Answer 11

I already did. But if you do not know how to determine the number of ways to choose 0 from a set of 7, or the number of ways to choose 1 from a set of 7; then you really need to go back and review that material. The rest of the setup is elementary ....

Answer 12

Can you solve the equation step by step @amistre64

Answer 13

not without having to try to teach you a chapters worth of material first.

consider this tho: if you have 7 things in front of you, what is the number of ways you can simply walk away and choose none of them?

Answer 14

\[\infty \] ways

Answer 15

:) there is really only 1 way to choose none of them, the choice to walk away is only 1 option.

7 "choose" 0 is equal to 1; in fact anything "choose" 0 = 1

Answer 16

how, consider these 7 things, but you can only choose one of them; how many ways is there to choose 1 of them?

Answer 17

7 ways

Answer 18

lets have 7 things to choose from: a b c d e f g

we can choose a
or we can choose b
or we can choose c
or we can choose d
or we can choose e
or we can choose f
or we can choose g

7 "choose" 1 is equal to ..7 do you agree?

Answer 19

oh, you do agree :) good.

Answer 20

now we can do the elementary stuff
\[ 1 - (1~.2^0~.8^7+7~.2^1~.8^6)\]

Answer 21

Ok so what will it be ?

Answer 22

most likely it will be whatever the calculator generates as an answer for you after you punch in the correct keys :/