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# probility of event

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a box contains 5 purple marbles, 3 green marbles and 2 orange marbles. two consecutive draws are made from the box withous replacement of the first draw what is the probability that the first marble is purple and the second is any color except purple.

Guest Feb 21, 2017

#1
+19645
+20

a box contains
5 purple marbles,
3 green marbles and
2 orange marbles.
two consecutive draws are made from the box withous replacement of the first draw
what is the probability that the first marble is purple and the second is any color except purple.

$$\begin{array}{|rcll|} \hline && \frac{5}{10} \cdot \frac{3}{9}+\frac{5}{10} \cdot \frac{2}{9} \\ &=& \frac{5}{10} \cdot \left( \frac{3}{9}+ \frac{2}{9} \right) \\ &=& \frac{5}{10} \cdot \frac{5}{9} \\ &=& \frac{25}{90} \\ &=& 0.2\bar{7} \quad (27.\bar{7}\ \%) \\ \hline \end{array}$$

heureka  Feb 21, 2017
#1
+19645
+20

a box contains
5 purple marbles,
3 green marbles and
2 orange marbles.
two consecutive draws are made from the box withous replacement of the first draw
what is the probability that the first marble is purple and the second is any color except purple.

$$\begin{array}{|rcll|} \hline && \frac{5}{10} \cdot \frac{3}{9}+\frac{5}{10} \cdot \frac{2}{9} \\ &=& \frac{5}{10} \cdot \left( \frac{3}{9}+ \frac{2}{9} \right) \\ &=& \frac{5}{10} \cdot \frac{5}{9} \\ &=& \frac{25}{90} \\ &=& 0.2\bar{7} \quad (27.\bar{7}\ \%) \\ \hline \end{array}$$

heureka  Feb 21, 2017