The diagram shows a board made from \(20\) identical squares, \(8\) of which are shaded. In a game a counter lands at random on one of these squares. The ga...
Question 1 Report
The diagram shows a board made from \(20\) identical squares, \(8\) of which are shaded.
In a game a counter lands at random on one of these squares.
The game is played \(150\) times.
Calculate the expected number of times the counter lands on a shaded square.
Answer Details
The counter lands at random on one of \(20\) identical squares, so each square is equally likely. With \(8\) of the squares shaded, the probability of landing on a shaded square is
\[ \frac{8}{20}=0.4 \]An expected frequency is that probability multiplied by the number of trials, and the game is played \(150\) times:
\[ \frac{8}{20}\times 150 \] [M1] \[ =0.4\times 150=60 \]The counter is expected to land on a shaded square \(60\) times [A1].
The squares being identical is the detail that makes each outcome equally likely; if they differed in size the probability could not be found by counting alone. As a check, the expected number of landings on the \(12\) unshaded squares is \(\frac{12}{20}\times 150=90\), and \(60+90=150\), the total number of games.
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