# Dart Games (SPM Additional Mathematics 2019)

I am a Form 4 student in Malaysia, which means that I am currently 16 years old, and there have been a few articles circulating about how difficult the questions in SPM (a national examination taken by Form 5 students) Additional Mathematics this year as compared to the questions the last few years. I tried solving some of them, but there were some that confused me. This is one of the questions in the exam,

Diagram 4 shows a dart's target board at a dart game booth in a funfair. The booth offers 3 darts per game. The customers have to pay RM 5 to play a game. A toy bear will be given to customers who are able to hit the bullseye for the three darts' throws in a game. Bob is a dart player. On average, he hits the bullseye 7 times out of 10 darts thrown.
1. Bob would play the game if he had at least 90% chance to win at least one toy bear by spending RM 30. By mathematical calculation, suggest to Bob whether he should play the game or otherwise. [7 marks]
2. What is the minimum number of games that Bob needed so that he can get 4 toy bears? [3 marks]

Any help would be appreciated, and there are a few more questions too I want to get help on.

Note by Tan Chin Cheern
7 months, 3 weeks ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

- 5 months, 2 weeks ago

There is a guaranteed win of 4 toy bears in 40 rounds i.e using 120 darts... and spending RM 800.

- 5 months, 2 weeks ago

The man has 99.7 % chance to win a toy bear in 6 games i.e spending RM 30.

- 5 months, 2 weeks ago

Do we need to hit all three darts to get a bear ? It's not clear in the question.... please tell me so that I might proceed further.

- 5 months, 2 weeks ago

I'd imagine the bear to be given when all 3 darts hit the bullseye. My approach to the first question would be to use binomial distributions to determine the probability of getting a bear. But then I'm stuck with the second question. How can I find the minimum number of games required using probability?

- 5 months, 2 weeks ago

I like your question, but I really do not know what to do..... but I want to try it out. If I find something, I will tell you.

- 5 months, 2 weeks ago