Math  /  Data & Statistics

Question1. Two balls are selected from a bowl containing 4 white balls, 2 green balls and 3 blue balls. Assuming that the selection is made randomly, one at a time with replacement, find the probability that (i) both balls are white. (ii) 2 different colors of balls.
2. A card is drawn from a deck of cards. The events A and B are defined as follows:

A: The selected card is a heart. BB : The selected card is a king. Find P(A),P(B)\mathrm{P}(\mathrm{A}), \mathrm{P}(\mathrm{B}) and P(AB)\mathrm{P}(\mathrm{A} \cap \mathrm{B}). State with reasons, if the events A and B are mutually exclusive events.
3. A box contains 3 blue marbles, 2 green marbles and 5 yellow marbles. 2 marbles are randomly drawn from the box one after the other with replacement. Find the probability of drawing (i) 2 blue marbles. (ii) 2 different colors of marbles.
4. The events AA and BB occur with probability P(A)=25P(A)=\frac{2}{5} and P(B)=14P(B)=\frac{1}{4}. Find P(AB)P(A \cup B) if the events (i) A and B are mutually exclusive, (ii) A and B are independent.
5. The three-year annual returns of 14 low-risk funds arranged in ascending order are given as follows. \begin{tabular}{|c|c|c|c|c|c|c|} \hline 9.77 & 11.35 & 12.46 & 13.80 & 15.47 & 17.48 & 18.37 \\ \hline 18.61 & 20.72 & 21.49 & 22.47 & 31.50 & 38.16 & 18.47 \\ \hline \end{tabular}

Find (i) the first quartile, (ii) the median, (iii) the third quartile.
6. A sample of 10 students in UITM showed the following credit hours taken during the first year of their programme. 17182118201922211824\begin{array}{llllllllll}17 & 18 & 21 & 18 & 20 & 19 & 22 & 21 & 18 & 24\end{array} Find (i) mean, (ii) the median, (iii) the third quartile.

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