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

• This Question is Open
1. amistre64 Group Title

there are 2 ways to approach this

2. amistre64 Group Title

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 Group Title

P(0) + P(1)

4. amistre64 Group Title

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

5. amistre64 Group Title

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 Group Title

@amistre64 how do we solve the equation ?

7. amistre64 Group Title

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 Group Title

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

9. amistre64 Group Title

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 Group Title

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

11. amistre64 Group Title

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 Group Title

Can you solve the equation step by step @amistre64

13. amistre64 Group Title

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 Group Title

$\infty$ ways

15. amistre64 Group Title

:) 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 Group Title

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 Group Title

7 ways

18. amistre64 Group Title

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 Group Title

oh, you do agree :) good.

20. amistre64 Group Title

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

21. Syamantak Group Title

Ok so what will it be ?

22. amistre64 Group Title

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