Binomial Probability help required (1 Viewer)

[4025808]

Man I swear I do not get a lot of the harder binomial probability questions =_=

Anyhow I did Fitzpatrick and I stumbled upon some questions
I seriously want to know how to do them but I don't know how to do them T_T

29 b)

Q13. A die is loaded such that in 10 independent trials the probability that an even number appears 5 times is twice the probability that an even number appears 4 times. What is the probability that an even number will appear in a single trial?
(Answer is 5/8)

Q15. The probability that persons aged 60 and 65 will survive the next year is 0.97 and 0.96 respectively. From a group of five people of whom three are aged 60 and two aged 65, what is the probability that
i) not more than one will die within the next year? (0.9893)
ii) the two aged 65 survive and not more than one dies within the next year? (0.9192)

Q16. How many times must a fair coin be tossed so that the probability of at least one head exceeds 0.9? (4)

grr I'm having difficulty with this topic

 

[laplace20]

13 is fairly basic lol

15 is conditional probability, which is slightly out of the hsc syllabus

16 is fairly easy once you see it done once, it is 2unit difficulty, it is by no means harder probability

but off course I am not gona do them : p

 

[4025808]

13 is fairly basic lol

15 is conditional probability, which is slightly out of the hsc syllabus

16 is fairly easy once you see it done once, it is 2unit difficulty, it is by no means harder probability

but off course I am not gona do them : p

lol why so slack for

 

[laplace20]

lol why so slack for

cuz I got replies lol

but those questions arent that hard

 

[laplace20]

lol 15 isnt conditional probability, I just read it real quick first time and thought it was.

but it doesnt look too hard.

lol Just got 15 figured out in like 2minutes

come on, if you cant do atleast 15 part i then you are really noob

 

[laplace20]

answer to 13 is definately correct : P

 

[4025808]

nvm i got 13 now... grr i didn't think about it properly T_T

 

[deterministic]

I will give tips and leave the rest to yourself
13) Let p be probability of even number. Give an expression for probability of even number appearing 5 times using binomial theorem. Do same for prob of even number appearing 4 times. Then use the fact P(even number 5 times)=2P(even number 4 times) to find p.

15) i) Consider 3 cases:
- probability that no one dies
- probability that a person aged 60 dies and people aged 65 live
- probability that a person aged 65 dies and people aged 60 live
then add them

ii) similar to part i) but exclude last case

16) Let n be the number of times a coin is tossed. Find an expression for the probability of at least 1 head for n tosses (use complimentary events to do so). That value needs to exceed 0.9. Then find n.

 

[elbatiolpxeho]

Q15. The probability that persons aged 60 and 65 will survive the next year is 0.97 and 0.96 respectively. From a group of five people of whom three are aged 60 and two aged 65, what is the probability that
i) not more than one will die within the next year? (0.9893)
ii) the two aged 65 survive and not more than one dies within the next year? (0.9192)

i) let p = probability of one surviving
   = P(a 60 year old survives) + P(a 65 year old survives)
   = 3/5*0.97 + 2/5*0.96
   = 0.966

  q = probability of one dying
   = 1 - 0.966
   = 0.034

  X = number of deaths

P(X≤1) = P(X=0) + P(X=1)
   = 5C0*0.966⁵ + 5C1*0.034*0.966⁴
   = 0.989

ii) P(both 65 year olds survive) = 0.96*0.96 = 0.9216

let p = probability of 60 year old surviving = 0.97

 q = probability of 60 year old dying = 0.03

 X = number of 60 year old deaths

P(65 y/o survive, X≤1) = 0.9216*[P(X=0) + P(X=1)]
          = 0.9216*(3C0*0.97³ + 3C1*0.03*0.97²)
          = 0.919

 

[elbatiolpxeho]

Shit... I just tried doing question 16 and realised I've forgotten most of this binomial stuff :O

Half-yearlies start on Monday :S

 

[blackops23]

binomials...? HALF YEARLIES??? Once again my school retains the reputation of being the slowest in Sydney.