GCSE Maths 2023 Paper 3 FINAL QUESTION

GCSE Maths 2023 Higher Paper 3 Final Grade 9 Question! (Probability tree diagrams, algebra, counters in a bag, fractions to ratio conversions, problem solving.)

In this video, we tackle a fascinating probability question involving counters in a bag. We'll guide you through the step-by-step process of solving this problem and finding the probability of selecting two counters of the same color.

The problem begins with a bag containing y counters, of which x are pink, five are blue, and the rest are green. The crucial information given is that the ratio of x to y is 1:3. We also know that there is no replacement, meaning once a counter is picked, it is not put back into the bag.

To approach this problem, we start by establishing relationships between the variables. By using the given ratio, we deduce that y equals 3x, simplifying the equation. Further analysis reveals that x + 5 + green equals y, which can be rewritten as x + 5 + green = 3x. We simplify this equation to green = 2x - 5.

With these relationships established, we construct a probability tree diagram, considering the three color options: pink, blue, and green. We examine the frequency of each color at each stage, accounting for the removal of a counter without replacement.

To determine the probability of selecting two counters of the same color, we focus on specific branches of the tree that lead to this outcome. We identify three combinations that satisfy the condition: pink-pink, blue-blue, and green-green.

Next, we express these combinations as algebraic expressions and set up the denominators for each branch of the tree. The denominator for the first choice is 3x, while the denominator for the second choice is 3x - 1, accounting for the counter already selected.

Finally, we simplify the expressions and combine them into a single fraction. Expanding brackets and collecting like terms, we arrive at a messy but solvable expression. We simplify further to obtain the final probability.

Join us in this tutorial as we solve this intriguing probability problem using probability tree diagrams. Gain a deeper understanding of how to approach similar questions and improve your GCSE Maths skills.

[senal]

im so happy i was able to do this now, for my mock they put a very similar question following the 2023 papers, but i couldnt do any of the last questions. now i am able to do all of them and i feel so confident for my paper 2 in like 4 days lol

[mancubsofficial]

Nice video! I think that this question was difficult because of where to start. Similar to the carrots and tomatoes question, people often forget that ratios can be converted into fractions! After that's figured out, and the overall layout of the problem is laid out, it's pretty smooth sailing. Great video! :)

[KabeerKhan-bvzw]

Love the fact that you solve the mathematical problems on a chalkboard.Dude istg it really fascinates me and reminds me of the time when numerous mathematical researches took place.

[pythonian]

Yay I'm pretty sure that I got this questjon right in my mock today

[klungoeatskettuce]

Could you maybe do the second to last question, about the tangents?

[Drippy_.]

petition to make your name “Sawtellium”