CIE S1 Book help on Probability and Expectation & Variance Questions

[whatsmyname]

Misc Ex 4, question no 8 page 81 - Probability:

P(A)=13/25, P(A')=12/25
P(B)=9/25, P(B')=16/25
P(A/B)=5/9 (<- conditional probability for A occuring given B has already occured),
P(B/A)=5/13, P(A and B)=1/5,

I could solve the question until here. Now, it asks for P(A or B or Both), P(A'/B') and to Determine P(A occurs or B does not occur) showing my workings. These three questions I cannot do, and would appreciate help on.

MIsc Ex 8, question no 2 page 131 - E(X) and Var(X)

Some of the eggs sold in a store are packed in boxes of 10, for any egg the Probability of it being cracked is 0.05, independent of other eggs. A shelf contains 80 of these boxes. Calculate the expected value of the number of boxes on shelf with no cracked egg -> Gotta find the E(X) of the number of boxes on the shelf that don't contain a cracked egg, but I would like someone to make the table for me as well just so I can clarify my doubts.

All help is appreciated, my sincere thanks in advance.

 

[whatsmyname]

ok the second one I solved and the crude solution looks like this:

P(E breaks)= 0.05 and Q(E breaks')= 0.95

1 box has 10 eggs, and probability of eggs breaking are independent, so using the Binomial Theorem, we can find probability of no eggs broken IN A BOX.

P(X=0) = 10C0 (.05)^0 x (0.95)^10 = 0.598

Then, we extrapolate and say for 80 boxes, EXPECTANCY of having no eggs broken, as given by n x p for any data following binomial, is = np = 80 x 0.598 = 47.9 ~ 48.

However, the second one is still not solved, except for A or B or Both. The answers are:
P(A or B or Both)= 17/25 [Found by using, P(A and B)=P(B) x P(A/B), and then a SETS formula AUB = A+B-ANB - P (A or B or Both)= P(A)+P(B)-P(A and B)]
P(A'/B')= 1/2
P(A occurs or B does not occur)= 21/25

 

[soumayya]

P(A'/B')= P(A' and B') /P(B')

P(A' and B')=1-P(AUB) =8/25

P(A'/B')=(8/25)/(16/15)=1/2

 

[soumayya]

P(A occurs or B does not occur) = P(A) + P(B') - P(A and B')
= 13/25 + 16/25 - 8/25 = 21/25

 

[soumayya]

u could use a venn diagram to check...

 

[svenas]

any body help in this question plz:
Bag A contains 3 red balls and 3 blue balls.
Bag B contains 1 red ball and 3 blue balls.
A ball is taken at random form bag A and placed in bag B . A ball is then chosen from bag B. What is the probability that the ball taken from B is red??

 

[Nikesh]

Here is the solution.......

 

[svenas]

Here is the solution.......

Thank u so much!

 

[Nikesh]

I have to thank you....coz you made me revise my AS course
keep on posting similar posts so that my revision process gets eased

 

[svenas]

I have to thank you....coz you made me revise my AS course
keep on posting similar posts so that my revision process gets eased

Here's another question:
Q) Give your answers to this question as fractions in their lowest terms. There are 21 students in a class. 12 are boys and 9 are girls. The teacher chooses two students at random.
(a)what is the probability that:
(i)both students are boys?
(ii)one is a boy and one is a girl?
(b)The teacher chooses a third student at random. What is the probability that atleast one of the three students is a girl?



(part (a) is easy for me, but (b) I can't solve;
Thanking you.

 

[Nikesh]

Here's another question:
Q) Give your answers to this question as fractions in their lowest terms. There are 21 students in a class. 12 are boys and 9 are girls. The teacher chooses two students at random.
(a)what is the probability that:
(i)both students are boys?
(ii)one is a boy and one is a girl?
(b)The teacher chooses a third student at random. What is the probability that atleast one of the three students is a girl?



(part (a) is easy for me, but (b) I can't solve;
Thanking you.

I think the process is correct so try to get it......here it is

 

[svenas]

I think the process is correct so try to get it......here it is

And the answer is completely correct, thank u my friend!!

 

[Nikesh]

its my pleasure dude

 

[svenas]

its my pleasure dude

here is another question, only part (dii) I didn't understand.
The answer for the last part is 0.0291.
Thanks...

 

[svenas]

I think the process is correct so try to get it......here it is

c this last question I sent u I already knew how to do it, I'll be sending other questions to u later....
BTW, because of u now I'm capable of solving most probability questions, as I was weak at this topic....thanks...

 

[Nikesh]

hahaha
keep on practicing u will achieve the highest confidence to solve the problems

 

[svenas]

hahaha
keep on practicing u will achieve the highest confidence to solve the problems

Here is a question about statistics:
only this part Which I sent I didn't understand, the answer is 2.5
Thanks..

 

[Nikesh]

sorry bro i could not get the question....
could you please paste the original copy of the question

 

[svenas]

sorry bro i could not get the question....
could you please paste the original copy of the question

ok

 

[svenas]

This is the full question ;