Binomial + probability qs

The question asked you have to expand (R+S)^5

The next question is , a four sided dice numbered from 1-4 . R represent the probability that the number four is rolled on a given roll and let S represent the probability that number 4 is NOT rolled on a given roll.

Use the 3 first terms of binomial expansion to find the probability that the number 4 is rolled atleast 3 times .


I have totally forgotten how to do probability and makes sense since I detested it . I just need guidance not answers . Do I need to construct a probability tree or something .

Thanks , right now I’m watching some videos on probability to help jog my memory

$(R+S)^5 = R^5 + 5R^4S + 10R^3S^2 + 10R^2 S^3 + 5R S^4 +S^5$

Since there's 4 sides and it doesnt say anything about it being an unfair die, you can assume that the die is fair hence R=0.25 and S=0.75.

Now for the probability that 4 is rolled atleast three times, we need R to happen 3, 4, or 5 times. These are precisely the powers of R which we need hence we only consider the first 3 terms of the expansion.

Have at it.

Sorry if I seem dumb.

Do I replace the value of r and s into the binomial expansion? I get everything but I still don’t know how I would use the information and apply it to the binomial. Why do we need the binomial . ( never had one of those questions before)
Edit: I was thinking of doing a probability tree

Sorry again ,

Yes you replace R and S in the binomial expansion.

You can draw a probability tree, but this is what the whole binomial deal is about - a tree is just a visual representation of it.

The tree also gets more and more cumbersome the more times you repeat an experiment as then you would need to consider more and more branches which can be done very quickly by considering the binomial.

As an example, this scenario is too much for a tree. Though if you want to consider it, then there would be 5 different sections for each throw: 1st throw, 2nd throw, etc... and by the time you get to the 5th row you would have 32 different branches to consider.

EDIT: Also, looking at the binomial, FYI the first term is the probability of rolling 4's five times out of five throws, the second term is the prob. of rolling 4's four times out of five, third term is rolling 4's three times out of five, etc...

Yes you replace R and S in the binomial expansion.

You can draw a probability tree, but this is what the whole binomial deal is about - a tree is just a visual representation of it.

The tree also gets more and more cumbersome the more times you repeat an experiment as then you would need to consider more and more branches which can be done very quickly by considering the binomial.

As an example, this scenario is too much for a tree. Though if you want to consider it, then there would be 5 different sections for each throw: 1st throw, 2nd throw, etc... and by the time you get to the 5th row you would have 32 different branches to consider.

EDIT: Also, looking at the binomial, FYI the first term is the probability of rolling 4's five times out of five throws, the second term is the prob. of rolling 4's four times out of five, third term is rolling 4's three times out of five, etc...

This is actually a question from one of the new Edexcel AS practice PURE papers. Surprise huh.

This is actually a question from one of the new Edexcel AS practice PURE papers. Surprise huh.

No way.
My teachers hasn’t told us this . Where can you get the questions from?

This is actually a question from one of the new Edexcel AS practice PURE papers. Surprise huh.