Question

1 multiple choice 4 points a bag contains 7 red balls and 3 white balls. andrew, betsy, cam and doug, in that order, are going to randomly pick a ball out of the bag and not replace it. the first person to draw a white ball wins $160. what is the probability that doug will win the $160? 1/4 1/8 3/40 1/7 2 multiple choice 4 points a bag has 6 red and 5 blue marbles. what is the probability of drawing a blue then a red, if the first marble is not replaced after it has been drawn? 9/30 3/11 7/29 11/29

Explanation:

Step1: Calculate probability for Doug in first problem

For Doug to win, Andrew, Betsy and Cam must all pick red - balls first. Initially, there are 7 red and 3 white balls (total 10 balls).
The probability that Andrew picks a red ball is $\frac{7}{10}$. After Andrew picks a red ball, there are 6 red and 3 white balls (total 9 balls). The probability that Betsy picks a red ball is $\frac{6}{9}$. After Betsy picks a red ball, there are 5 red and 3 white balls (total 8 balls). The probability that Cam picks a red ball is $\frac{5}{8}$. After Cam picks a red ball, there are 4 red and 3 white balls (total 7 balls). The probability that Doug picks a white ball is $\frac{3}{7}$.
The combined probability is $\frac{7}{10}\times\frac{6}{9}\times\frac{5}{8}\times\frac{3}{7}=\frac{7\times6\times5\times3}{10\times9\times8\times7}=\frac{1}{8}$.

Step2: Calculate probability for second problem

The probability of drawing a blue ball first is $\frac{5}{6 + 5}=\frac{5}{11}$. After drawing a blue ball, there are 6 red and 4 blue balls (total 10 balls). The probability of drawing a red ball second is $\frac{6}{10}=\frac{3}{5}$.
The combined probability of drawing a blue then a red is $\frac{5}{11}\times\frac{3}{5}=\frac{3}{11}$.

Answer:

1. B. $\frac{1}{8}$
2. B. $\frac{3}{11}$