N2014 P2 Q10
N2014 P2 Q10
Junior College 2
10 marks
A game uses the following three sets of \(10\) symbols.
| Set 1 | + | + | + | + | \(\times\) | \(\times\) | \(\times\) | \(\circ\) | \(\circ\) | * |
| Set 2 | + | + | + | \(\times\) | \(\circ\) | \(\circ\) | \(\circ\) | \(\circ\) | * | * |
| Set 3 | + | + | \(\times\) | \(\times\) | \(\times\) | \(\times\) | \(\circ\) | \(\circ\) | \(\circ\) | * |
One symbol is chosen at random from each set. For example, choosing \(+\) from Set 1, \(\circ\) from Set 2 and \(*\) from Set 3 gives \(+\circ*\).
- Find the probability that the three symbols chosen are
- three stars,[1]
- at least one star,[2]
- two crosses and one plus, in any order.[3]
- Given that exactly one of the symbols chosen is a star, find the probability that the other two symbols are a plus and a circle.[4]
Solution:
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Answer:(i)(a) \(0.002\), (b) \(0.352\), (c) \(0.058\). (ii) \(\frac{71}{306}\approx0.232\).
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