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.

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Math

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2^{34}

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\frac{2}{3}

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\sqrt{2}

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\sum_{i=1}^3

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

Math	Appears 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}`	$\boxed{123}$

Comments

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.

Nikola Alfredi - 1 year, 4 months 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?

Tan Chin Cheern - 1 year, 3 months 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.

Nikola Alfredi - 1 year, 3 months ago

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

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

Post the other questions or share the link if already posted....

Yes, the task is not an easy one. I tried to pass this test more than once. Unfortunately, or maybe, fortunately, these attempts gave some experience.

Morgan Wright - 6 months, 3 weeks ago

Math	Appears 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}`	$\boxed{123}$