Maths question

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# Maths question Posts: 26
Legend A2 Maths, A2 Chemistry, A2 Biology, LSC Queensbury
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(@splum5)
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Joined: 3 years ago

This question came up on an exam I had on Monday and I answered it but I won’t be getting the test back for a while and I’m really anxious to see if I got it correct.

second part of this question.

The questions state as follows:

4.A.

fully expand (p+q)^5

I have done this, using the binomial expansion theorem and have gotten an answer of:

p^5 +5p^4q + 10p^3q^2 + 10p^2q^3 + 5pq^4 + q^5

B.

a fair 4 sided die, numbered 1, 2, 3, and 4, is rolled 5 times. Let p represent the probability that the number 4 is rolled on a given roll, and let q represent the probability that the number 4 is not rolled on a given roll.

Using the first 3 terms of the binomial expansion from part a, find the probability that the number 4 is rolled at least 3 times.

How do I answer part B?

Thank you

6 Replies (@zeeshan)
Joined: 4 years ago

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Posts: 770

@splum5

The part (a) is the topic binomial expansion

whereas part (b) is called binomial distribution - stats and mechanics chapter 6.

If you haven't covered binomial distribution before, you could say it was a bit of an unfair question to give, however this is how you would do it.

Basically p would represent the probability of getting a 4 (which is 1/4) and q would represent the probability of not getting a 4 (which is 3/4)

And because it says use the first 3 terms of the binomial expansion, you basically fill in p = 1/3 and q = 1/4 into the "the first 3 terms", p^5 +5p^4q + 10p^3q^2.

so (1/4)^5 + 5 (1/4)^4 (3/4) + 10 (1/4)^3 (3/4)^2

Again, if you havent gone over chapter 6 in stats and mechanics yet in school - i wouldn't worry too much about this question just yet Posts: 76
(@hrashid_)
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Joined: 4 years ago

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@hrashid_

(i) I would substitute root a = b

Because now you get a^2 = b^4

so the equation becomes 16b^4 = 2b

Then to solve that

16b^4 - 2b = 0

(b)(16b^3 - 2) = 0

so b =0 and b = 1/2

But remember we said b = root a

so actually root a = 0 and root a = 1/2

so a = 0 and a = 1/4

Do the same thing for part (ii)  but substitute a = b^2

To turn it into a^2 + 7a - 18 = 0 then etc

For more practice go to exercise 2E, question 7 (@hrashid_)
Joined: 3 years ago

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(@hrashid_)
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Joined: 3 years ago (@zeeshan)
Joined: 4 years ago

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Posts: 770

@hrashid_

They basically just saying coordinates but in context

so that "3 years after planting, height was 2.35 metres" just means a coordinate was (3, 2.35)

They also gave you the other coordinate, so just work out y = mx + c

Then part (b) is saying the "initial value" is 140cm, just compare that with your y-intercept and see if its really far away or close to it

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