# 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, 1 week ago

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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 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?

- 4 months, 4 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.

- 4 months, 4 weeks ago

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

- 4 months, 4 weeks ago

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

- 4 months, 4 weeks ago