Lots of questions that I've tried and gotten stuck on. I'll post the questions and my answers to them
1) Fully simplify
I got I think that's right.
2) Nicolas has 30 beads in a bag. 9 of them are white. 8 green. 13 blue. What is the probability that if two beads are taken from the bag at random that they will not be the same colour. I got Definitely wrong
3)OPR is a triangle. OP = p and OR = r
a.Find the vector PR in terms of p and r
(No answer, I tried it but I just got stuck)
A os a point on PR such that PA:AR=7:2
b. Show that OA =
Again I tried but couldn't even get close to an answer...
4)Prove that, for all positive integer values of n, is a multiple of 2.
Here I found out why but I just don't know how to word it so an exam will accept it...
Ok thank you for explaining the second but I am still confused to the first one. Why do you label certain probabilities as something such as 8c-subscript-2?
I'm quite surprised with your answer because this was quite an early question in a GCSE paper and probably the hardest one looking at the answer.
You probably have and buttons
on your calculator.
will calculate the number of ways of arranging r items from a total of N.
will count the number of ways of selecting (without arranging) r items from N.
Using those keys is the fastest way to answer.
The probability of selecting 2 beads the same is
The probability of the beads being different is that subtracted from 1.
Here's an alternative...
Probability of 2 whites in a row is
Probability of 2 greens in a row is
Probability of 2 blues in a row is
The probability of getting 2 beads the same colour is the sum of these 3 probabilities, since we can get 2 whites, 2 greens or 2 blues.
Since all the probabilities of the situation of drawing 2 beads must sum to 1, all you need do is subtract the sum of those 3 from 1,
in order to find the probability that the first 2 beads will be of different colours.
Remember, if the first bead is white, there are 29 beads left and 8 are white,
ie one less bead and one less white.
Same for the others.
It might have helped if I'd checked how you got that value!
However, this was useful in that there is an alternative with those calculator buttons, especially when you need to check something like 17 out of 30.
For large numbers the keys are very very fast.
Thank you for your patience too, good work.