Am stuck on "There are 1000 people 200 of them are boys (20%) You randomly..."

[philD]

Am stuck on "There are 1000 people 200 of them are boys (20%) You randomly..."

Hello, can someone help me with this please?!!

There are 1000 people


200 of them are boys (20%)


You randomly select 35% i.e. 350 of the 1000 people


Q)
a) What is the probability that you will get a boy and
b) How many boys are you likely to get on average in the 350​ (35% of 1000) randomly selected​
?




Must be a probability​ and average ​
equation​ for it​
?



I don't think it can be that 1 in 5 are boys (20%) therefore 350 x 20% = 70 boys
Because if you chose to select 35% of the 200 boys only and exclusively, you would also get 70 (200 x 35% = 70)

The answer to Q) has to be much lower than 70

Would it be 35% of 20% = 7% so it would be 200 x 7% = 14 boys?


Any idea?

 

[Harry_the_cat]

Hello, can someone help me with this please?!!

There are 1000 people

200 of them are boys (20%)

You randomly select 35% i.e. 350 of the 1000 people

Q)
a) What is the probability that you will get a boy and
b) How many boys are you likely to get on average in the 350​ (35% of 1000) randomly selected​
?

Must be a probability​ and average ​
equation​ for it​
?

I don't think it can be that 1 in 5 are boys (20%) therefore 350 x 20% = 70 boys
Because if you chose to select 35% of the 200 boys only and exclusively, you would also get 70 (200 x 35% = 70)

The answer to Q) has to be much lower than 70

Would it be 35% of 20% = 7% so it would be 200 x 7% = 14 boys?


Any idea?

Does the question "What is the probability that you will get a boy" mean the probability of getting at least one boy in the 350 people you select?

If so, then the number of boys forms a binomial distribution with p=0.2, q=0.8 and n=350.

P(at least 1 boy) = 1 - P(no boys) = 1 - P(all girls) = 1 - (0.8)^350 = 1 - 1.2*10^-34 which is very close to 1.

P(exactly one boy) = 350 * (0.2)^1 * (0.8)^349 = 1.0556 * 10^-32 (which is very, very small)

For b) If 20% of the population are boys, then you would expect 20% of your random selection to be boys, so you would expect 20% of 350 = 70 boys.

 

[philD]

thnaks

does the question "what is the probability that you will get a boy" mean the probability of getting at least one boy in the 350 people you select?

If so, then the number of boys forms a binomial distribution with p=0.2, q=0.8 and n=350.

P(at least 1 boy) = 1 - p(no boys) = 1 - p(all girls) = 1 - (0.8)^350 = 1 - 1.2*10^-34 which is very close to 1.

P(exactly one boy) = 350 * (0.2)^1 * (0.8)^349 = 1.0556 * 10^-32 (which is very, very small)

for b) if 20% of the population are boys, then you would expect 20% of your random selection to be boys, so you would expect 20% of 350 = 70 boys.

thanks, as i see it that couldn't be true, for example if i randomly select 35% of the list of 200 boys only i will definitely get 70
but if i randomly select 35% of the list of 1000, from within where only 200 are boys, i will get a random 350 (leaving 650) so the 200 boys could all fall within the 650 and i get none, or the 200 boys all fall within the 350, or part thereof etc, so the likely/probable result could not possibly be the same/identical, ie 70, it would have to be less (much less) when we randomly select from the 1000 people where only 20% (200) are boys ?
Hence why i think it could be 35% of 205 = 7% of 200 = 14

thoughts?
Thanks!