Respuesta :
We are given the following information.
White marbles = 2
Black marbles = 3
Red marbles = 1
Blue marbles = 4
The total number of marbles are
Total marbles = 2+3+1+4 = 10
Cade selects two marbles from the bag at random with replacement.
The probability of selecting a blue marble is given by
[tex]P(blue)=\frac{blue\;marbles}{total\;marbles}=\frac{4}{10}=\frac{2}{5}[/tex]The probability of selecting a black marble is given by
[tex]P(black)=\frac{black\;marbles}{total\;marbles}=\frac{3}{10}[/tex]The probability of selecting a blue marble followed by a black marble is given by
[tex]\begin{gathered} P(blue\;and\;black)=P(blue)\times P(black \\ P(blue\;and\;black)=\frac{2}{5}\times\frac{3}{10}=\frac{6}{50}=\frac{3}{25} \end{gathered}[/tex]So, the probability of selecting a blue marble followed by a black marble is 3/25
He does this a total of 30 times.
[tex]\frac{3}{25}\times30=3.6[/tex]Therefore, the reasonable prediction for the number of times he will select a blue marble followed by a black marble is 3.6 times.
