Question

You are given a bag that contains 7 red, 8 blue, 2 orange, 3 white, and 6 green marbles.1) What is the probability of selecting a red marble replacing it and then selecting a green marble?2) What is the probability of selecting a blue marble replacing it and then selecting another blue marble?3) What is the probability of selecting a white marble and then a green marble without replacing the first marble?4) What is the probability of selecting a red marble and then selecting another red marble without replacing the first marble?

Answer 1

replacementThe marbles given are

$\begin{gathered} \text{RED}=7 \\ \text{BLUE}=8 \\ \text{ORANGE}=2 \\ \text{WHITE}=3 \\ \text{GREEN}=6 \end{gathered}$

The total number of marbles will be

$7+8+2+3+6=26$

1) To calculate the probability of selecting a red marble replacing it and then selecting a green marble

$\begin{gathered} Pr(\text{red)}=\frac{Number\text{ of red}}{\text{Total number of marbles}} \\ Pr(\text{red)}=\frac{7}{26} \\ Pr(\text{green)}=\frac{Number\text{ of gr}een}{\text{total number of marbles}} \\ Pr(\text{green)}=\frac{6}{26}(\text{with replacement)} \\ \text{therefore}, \\ Pr(\text{red and gre}en)=Pr(red)\times Pr(green) \\ Pr(\text{red and gre}en)=\frac{7}{26}\times\frac{6}{26} \\ Pr(\text{red and gr}een)=\frac{21}{338} \end{gathered}$

Hence,

The probability of selecting a red marble replacing it and then selecting a

green marble is 21/338

2) To calculate the probability of selecting a blue marble replacing it and then selecting another blue marble

$\begin{gathered} Pr(blue\text{)}=\frac{Number\text{ of blue}}{\text{Total number of marbles}} \\ Pr(\text{blue)}=\frac{8}{26} \\ \text{with replacement the probabilty of picking a second blue marble will be the}8 \\ Pr(\text{second blue)=}\frac{8}{26} \\ Pr(\text{blue and blue)=}\frac{8}{26}\times\frac{8}{26} \\ Pr(\text{blue and blue)=}\frac{16}{169} \end{gathered}$

Hence,

The probability of selecting a blue marble replacing it and then selecting another blue marble is 16/169

3) To calculate the probability of selecting a white marble and then selecting a green marble without replacing the first marble

$\begin{gathered} Pr(white\text{)}=\frac{Number\text{ of white}}{\text{Total number of marbles}} \\ Pr(\text{white)}=\frac{3}{26} \\ \text{without replacement the toal number of marbles reduces from 26 to 25} \\ \text{therefore,} \\ Pr(\text{green)}=\frac{Number\text{ of green}}{\text{Total number of remaining marbles}} \\ Pr(\text{green)}=\frac{6}{25} \\ \text{Hence,} \\ Pr(\text{white and gre}en\text{ without replacement)=}\frac{3}{26}\times\frac{6}{25}=\frac{9}{325} \end{gathered}$

Hence,

The probability of selecting a white marble and then selecting a green marble without replacing the first is 9/325

4) To calculate the probability of selecting a red marble and then selecting another red marble without replacing the first marble

$\begin{gathered} Pr(\text{red)}=\frac{Number\text{ of red}}{\text{Total number of marbles}} \\ Pr(\text{red)}=\frac{7}{26} \\ \text{without replacement the toal number of marbles reduces from 26 to 25} \\ \text{While the number of red reduces from 7 to 6. } \\ \text{therefore,} \\ Pr(\text{another red without replcaement)=}\frac{6}{25} \\ Pr(\text{red and red without replacement)=}\frac{7}{26}\times\frac{6}{25}=\frac{21}{325} \end{gathered}$

Hence,

The probability of selecting a red marble and then selecting another red marble without replacing the first marble is 21/325