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2. ### Probability question on fair coin

then 1 - 0.52 = 3/4
3. ### Probability question on fair coin

so the probability of getting HH is p2? Then the required probability is 1- p2?
4. ### Probability question on fair coin

If it is HT, then no matter the next one is T or H, TH already occurs before HH, right? If it is TT, then also no matter the next one is T or H, TH already occurs before HH, right? If it is TH, then obviously no matter the next one is T or H, TH already occurs before HH, right? Just the case if...
5. ### Probability question on fair coin

so if there is no HH, then it is alright? Let the probability of getting a H be p. Then the required prob. is 1 - p2?
6. ### Probability question on fair coin

Actually TT, HT,TH all means TH must occur before HH, right?
7. ### Probability question on fair coin

Should I indeed use conditional probability? In case I have a T at the 1st trial, then it already achieves the event that TH appears before HH?
8. ### Probability question on fair coin

Oh Sorry... I have a typo in the question... The correct question is "T,H before HH"
9. ### Probability question on fair coin

but it seems 0.5*0.5*0.5*... , gets you 0...

1?
11. ### Probability question on fair coin

Which two? TH and HT? 0.5*0.5 + 0.5*0.5 = 0.5?
12. ### Probability question on fair coin

So simply calculate the first case?

Same?
14. ### Probability question on fair coin

I don't quite understand your question... The prob. of getting a head or a tail is 1/2? Is this what you are asking?
15. ### Probability question on fair coin

Homework Statement A fair coin is continually flipped. What is the probability that the pattern T,H occurs before the pattern H,H, where T and H respectively denote Tail and Head of a coin? Homework Equations Prob. = (n r) (pr)(1-p)n-r The Attempt at a Solution I am thinking whether the...
16. ### Probability and normal distribution

because question 1 is P(acceptable)...so I use it directly...
17. ### Probability and normal distribution

So is this P(more than 2 tests) = 1 - [ P(1st acceptable) + P(1st rejected, 2nd accpetable) ] = 1 - [ p + (1-p)p ] wrong?
18. ### Probability and normal distribution

I understand 1st and 3rd question now. For 2nd question, my approach now is let p be the P(accpetable) in 1st question. P(more than 2 tests) = 1 - [ P(1st acceptable) + P(1st rejected, 2nd accpetable) ] = 1 - [ p + (1-p)p ]. Is this correct?
19. ### Probability and normal distribution

Homework Statement Due to the pollution from the industry around an apple farm, the apples grown there may be contaminated by heavy metals. It is believed that the amount of heavy metals in an apple of the farm follows the Normal distribution. N(16,16) which has a mean μ = 16 units and σ = √16...
20. ### Prove arcsin x for its logarithm form

Homework Statement Given sin x = (eix - e-ix) / 2i, I want to prove that arcsin x = -i ln(ix + √1 - x2) Homework Equations I know about the Euler's formula and complex number. But I have never learnt about complex logarithms. The Attempt at a Solution I try to use x = sin y. But it seems...
21. ### Decomposition using roots of unity

Sorry. My typo... It should be (e2πi/5)5, so it equals 1.
22. ### Decomposition using roots of unity

I can solve it now. Thanks.
23. ### Decomposition using roots of unity

You mean I can make two pairs into the form (x−r)(x−r∗) that makes them real?
24. ### Decomposition using roots of unity

You mean this pair are conjugates to each other?
25. ### Decomposition using roots of unity

I can get (x - 1)(x4 + x3 + x2 + x + 1), but then what to do? To decompose (x4 + x3 + x2 + x + 1) into 2 more?
26. ### Decomposition using roots of unity

Homework Statement Decompose x5 - 1 into the product of 3 polynomials with real coefficients, using roots of unity. Homework Equations As far as I know, for xn = 1 for all n ∈ ℤ, there exist n distinct roots. The Attempt at a Solution [/B] So, let ω = e2πi/5. I can therefore find all the 5th...