**I/GCSE** **Mathematics**** Question Analysis Topic: Mathematics - Short Questions**

**Exam Question:**

1) Find the distance between the planes 2x−y+2z=5 and 5x−2.5y+5z=20.

2) A die, whose faces are marked 1,2,3 in red and 4,5,6 in green, is tossed. Let A be the event "number obtained is even" and B be the event "number obtained is red". Find if A and B are independent events.

**Answer:**

For I/GCSE Mathematics, you should know:

1) With two **parallel **planes of forms:

ax + by + cz = **d**_{1}, and

ax + by + cz = **d**_{2}, the **distance **between them is

|d_{1} - d_{2}| / **sqrt**(a^{2} + b^{2} + c^{2})

5x - 2.5y + 5z = 20**Factorize **--> 2.5(2x - y + 2z) = 2.5 x 8

--> Second equation written as: **2x - y + 2z = 8**

As such, the distance between the two planes is

**|8 - 5| / sqrt(2**^{2}** + 1**^{2}** + 2**^{2}**) = 1 unit.**

2) With regards to the information given,**A = {2, 4, 6}B = {1, 2, 3}**

Therefore A∩B = {2}

**P(A**

**∩B) = 1/6**

**and**

P(A) = 1/2

P(A) = 1/2

**P(B) = 1/2**

Multiplying these together, we have:

P(A) * P(B) = 1/4 **=/= **P(A∩B)

As such, we know that A and B are **independent **events.

Work hard for your I/GCSE Mathematics examination!

End of analysis. Great!