Questions on Binomial Probability (1 Viewer)

[Dimsimmer]

1. 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 in a single trial?

2.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 is aged 60 and two aged 65, what is the probability that (i) not more than one will die within the next year, (ii) the two aged 65 will survive and not more than one does within the next year?

3.In an examination consisting of ten true-false questions, a student guesses the answers. What is the probability that he will gain 70% or better?

Thanks guys for your help.

 

[Riviet]

3. p(70% or better)=p(70%) + p(80%) + p(90%) + p(100%)
=(10C7)/2¹⁰ + (10C8)/2¹⁰ + (10C9)/2¹⁰ + (10C10)/2¹⁰
=0.17 (2 dp)

 

[gamecw]

lol i dont like typing here Q1
http://img134.imageshack.us/my.php?image=math1me0.jpg

ooops made a mistake!

read webby234's or heres the edited one

http://img246.imageshack.us/img246/552/maths2vi9.jpg

 

[webby234]

1. Let a be the probablity an even number appears in an independant trial and b be the probability of an odd number.

(a + b)¹⁰
= a¹⁰ + ... + 10C4 a⁴b⁶ + 10C5 a^{5[/sup[bsup]5}...+ b¹⁰

10C5 a⁵b⁵ = 2*10C4 a⁴b⁶

3a = 5b
a + b = 1 (as a and b are the only two possibilities)

3 - 3b = 5b
b = 3/8
a = 5/8

 

[gamecw]

2. (i) not more than one will die within the next year

60 die - 0.03, 65 die - 0.04

not more than one will die:
1. 1 of 60 dies, 65 all live
2. 1 of 65 dies, 60 all live
3. all live!

1. 3C1 x (0.97^2) x (0.03) x (0.96^2) = 0.078
2. (0.97^3) x 2C1 (0.96) (0.04) = 0.07
3. (0.97^3) (0.96^2) = 0.841

Therefore, prob = 0.078+0.07+0.84 =0.989

mm i think..

Edit:
hey part two of 2 doesnt make sense to me
(ii) the two aged 65 will survive and not more than one does within the next year?

If the statement already says two will survive, then how to work out 'not more than one does (surrvive)' for it? unless its a typo its 'dies' or not 'does'?

If im right then for (ii):

Prob = 0.078 + 0.841 = 0.919

 

[Dimsimmer]

Yeh part (ii) of two was a typo. Its actually 'dies', not 'does' so you are right.