Answer:
The expected number of times a red marble will be selected is 12.
Step-by-step explanation:
The number of marbles in a bag are:
Yellow = 4
Red = 3
Blue = 1
Total = 8
Le the random variable X be defined as the number of red marble selected.
The probability of selecting a red marble is:
[tex]P(red)=\frac{3}{8}[/tex]
A marble is selected from the bag n = 32 times.
The color of the marble selected at the nth draw is independent of the previous draw.
The success is defined as selecting a red marble.
The random variable X thus follows a Binomial distribution with parameters n = 32 and p = [tex]\frac{3}{8}[/tex].
The expected value of a Binomial random variable is:
[tex]E(X)=np[/tex]
Compute the expected number of times a red marble will be selected in 32 draws as follows:
[tex]E(X)=np[/tex]
[tex]=32\times\frac{3}{8}\\=12[/tex]
Thus, the expected number of times a red marble will be selected is 12.
