1. ## Probability help.....plezz

hi just started stats at uni and having a little trouble getting sum questions like the one below any help would be great thanks.

Records show that 35% of the students successfully completing STAT111 also do MATH108 as part of their degree.
A group of 10 students is selected at random. Find the probability that:

(1) None of a randomly selected group of 10 students successfully completing STAT111 also do MATH108 as part of their degree.

(2) Less than half of the group of 10 students successfully completing STAT111 also do MATH108 as part of their degree.

2. Originally Posted by skippy101
hi just started stats at uni and having a little trouble getting sum questions like the one below any help would be great thanks.

Records show that 35% of the students successfully completing STAT111 also do MATH108 as part of their degree.
A group of 10 students is selected at random. Find the probability that:

(1) None of a randomly selected group of 10 students successfully completing STAT111 also do MATH108 as part of their degree.

(2) Less than half of the group of 10 students successfully completing STAT111 also do MATH108 as part of their degree.
Good evening Skippy,

Think of it this way, you have 2 events, success being a student who passes STAT111 also takes the course MATH108. This is p which is the probability of success.

You also have q, which is 1 - p, which is failure. That is 0.65, and that represents a student who passes STAT111 that does not take MATH108. That sounds like a binomial distribution. Since n = 10 which is small, we can skip doing the Poisson approximation to the binomial distribution.

For question A, you want the probability that exactly 0 successes occur. For the answer, the math, and all the sugar coated toppings, go here:

Binomial Distribution

We already determined n is 10, p is 0.35, and for k, we want exactly k successess, k being 0. So, enter those 3 items, press the first button "exactly k successes" and check out the answer and the math.

I get 0.0135 rounding to 4 digits. Does that make sense?

Now for question b.

This time, they ask for "Less than half of the group of 10 students". n and p are still the same, nothing has changed there. 1/2 of 10 is 5. But they say "less than", not "less than or equal to" or "no more than". Less than 5 in integer terms means <= 4. We want P(x <= 4).

Go back to the same link:

Binomial Distribution

n and p are the same from question a, but now, our k is 4. Press the 2nd button, "no more than k successes". I get 0.7516. Scroll down slowly and you will see each probability calculated for x = 0,1,2,3,4. Then check out the cumulative probability section towards the bottom. Notice that our probability for x = 0 matches our answer in question a.

Any questions?

3. If your answer for b does not match, they may have worded it in a way that mean "1/2 or less". Let me know if the answer does not match, we can figure it out together.

4. hey thanks alot that helped heapz cheers mate

5. and yes i got the same answers as you