9. Engineering Probability and Statistics#
Contributor
Dr. Wenjie Fei created the annotated review notes.
Readings#
Videos#
Example#
What is the probability of picking an orange ball and a white ball out of a bag containing seven orange balls, eight green balls, and two white balls?
(A) 0.071
(B) 0.103
(C) 0.360
(D) 0.536
Work it Out#
Problem: A bag contains 7 orange, 8 green, and 2 white balls. Two balls are drawn (without replacement). What is the probability of drawing one orange and one white?
Step 1: Total number of balls#
\(7+8+2=17\)
Total ways to choose 2 balls:
\(\binom{17}{2}= \frac{17 \times 16}{2} = 136\)
Step 2: Favorable outcomes (1 orange, 1 white)#
Ways to pick 1 orange: \(\binom{7}{1}=7\)
Ways to pick 1 white: \(\binom{2}{1} = 2\)
So favorable outcomes = \(7×2=14\).
Step 3: Probability#
\(P(\text{1 orange and 1 white})=\frac{14}{136}=\frac{7}{68}~\approx~ 0.103\)
Choose B