Probability :( (1 Viewer)

[Inexorably Me]

Hey guys, I REALLY suck at probability and i was wondering if anyone could help me with this Q: In a certain strain of plants, probability of seeds producing pink flowers is 0.25. Determine the least no. of seeds that must be planted to give a probability of pink flowers which exceeds 0.99. (Ans: 77).
I don't get how to work with Q's like these. *FAIL*

 

[AlexJB]

Are you sure the answer is 77 not 17?

 

[Inexorably Me]

LOL, thats what the answers say. Must be a typo then. But could you tell me how to work it out please? =\

 

[Drongoski]

Are you sure the answer is 77 not 17?

Looks like 17 to me too.

 

[scardizzle]

P(atleast 1 pink flower) = 1 - P(no pink flowers)

= 1 - (0.75)^n

to exceed .99

1 - (0.75)^n > 0.99

therefore

0.01 > (0.75)^n

therefore ln(0.01) > n x ln(0.75)

therefore n > ln(0.01)/ln(0.75)

therefore n > 16.00784...

therefore n = 17

 

[untouchablecuz]

P(atleast 1 pink flower) = 1 - P(no pink flowers)

= 1 - (0.75)^n

to exceed .99

1 - (0.75)^n > 0.99

therefore

0.01 > (0.75)^n

therefore ln(0.01) > n x ln(0.75)

therefore n > ln(0.01)/ln(0.75)

therefore n > 16.00784...

therefore n = 17

not completely correct

0.01 > (0.75)ⁿ

Ln(0.01) < Ln(0.75)ⁿ

Ln(0.01) < nLn(0.75)

nLn(0.75) > Ln(0.01)

n > Ln(0.01)/Ln(0.75) ~ 16.00748 ~ 17

 

[Inexorably Me]

*hails* thanks again