17M.2.SL.TZ2.S_B10

pestleMathematicsAISLPaper 217M· sl-4-5-probability-concepts-expected-numberssource ↗

The following table shows a probability distribution for the random variable $X$ , where ${\text{E}}(X) = 1.2$ .

M17/5/MATME/SP2/ENG/TZ2/10

A bag contains white and blue marbles, with at least three of each colour. Three marbles are drawn from the bag, without replacement. The number of blue marbles drawn is given by the random variable $X$ .

A game is played in which three marbles are drawn from the bag of ten marbles, without replacement. A player wins a prize if three white marbles are drawn.

Jill plays the game nine times. Find the probability that she wins exactly two prizes.

Markscheme / solution

valid approach (M1)

eg $\,\,\,\,\,$ ${\text{B}}(n,{\text{ }}p),{\text{ }}\left( {\begin{array}{*{20}{c}} n \\ r \end{array}} \right){p^r}{q^{n - r}},{\text{ }}{(0.167)^2}{(0.833)^7},{\text{ }}\left( {\begin{array}{*{20}{c}} 9 \\ 2 \end{array}} \right)$

0.279081

0.279 A1 N2

[2 marks]

Examiners’ report

[N/A]