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

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1. amistre64

there are 2 ways to approach this

2. amistre64

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)

3. amistre64

P(0) + P(1)

4. amistre64

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

5. amistre64

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: $\sum_{2}^{7}~\binom{7}{r}~.2^r~.8^{7-r}$

6. Syamantak

@amistre64 how do we solve the equation ?

7. amistre64

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

8. Syamantak

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

9. amistre64

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?

10. Syamantak

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

11. amistre64

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 ....

12. Syamantak

Can you solve the equation step by step @amistre64

13. amistre64

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?

14. Syamantak

$\infty$ ways

15. amistre64

:) 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

16. amistre64

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

17. Syamantak

7 ways

18. amistre64

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?

19. amistre64

oh, you do agree :) good.

20. amistre64

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

21. Syamantak

Ok so what will it be ?

22. amistre64

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