Help please - Binomial Probability (1 Viewer)

[x-kendall-x]

Hey !
Can anyone possibly help me out with some questions on binomial probability?
I have trouble at the best of times with it but I'm struggling immensely at the moment.

1. It is known that 7 out of every 10 students from Yr 12 at a school will enter uni. Assuming a binomial distribution, find the probability that out of a group of 5 students chosen at random only the first 3 chosen will enter?

2. A dental inspector finds that about 20% of children have tooth decay. What is the probability that out of 6 children examined, only the first, third and fifth will have tooth decay?



Any help would be amazing
thankyou !

 

[redflyer]

1) probability of success(going to uni) = 0.7
Let X (random variable) = number of students chosen to go to universityfrom the group of five people

first three chosen will enter, hence:

1st chosen: enter
2nd chosen: enter
3rd chosen: enter
4th chosen: not enter
5th chosen: not enter

Because we are given a specific probility order we can do it via this method:

= 0.7 x 0.7 x 0.7 x 0.3 x 0.3
= (0.7)^3 x (0.3)^2
= 0.03087

2)Probility of success(will have tooth decay) = 0.2
Let X = number of children having tooth decay in the group of 6 children

Order is given hence:

1st children = have tooth decay
2nd children = DON'T have tooth decay
3rd children = have tooth decay
4th children = DON'T have tooth decay
5th children = have tooth decay
6th children = DON'T have tooth decay

Therefore, going through each children, we multiply their probability of obtaining tooth decay:

= 0.2 x 0.8 x 0.2 x 0.8 x 0.2 x 0.8
= (0.2)^3 x (0.8)^3
= 0.004096

I hope this makes sense!

 

[x-kendall-x]

ohhhhh

thankyou so much thats helps heaps. You have no idea !