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
<u> Blue = 1 </u>
Total = 8
Le the random variable <em>X</em> be defined as the number of red marble selected.
The probability of selecting a red marble is:
A marble is selected from the bag <em>n</em> = 32 times.
The color of the marble selected at the <em>n</em>th draw is independent of the previous draw.
The success is defined as selecting a red marble.
The random variable <em>X</em> thus follows a Binomial distribution with parameters <em>n </em>= 32 and <em>p</em> = .
The expected value of a Binomial random variable is:
Compute the expected number of times a red marble will be selected in 32 draws as follows:
Thus, the expected number of times a red marble will be selected is 12.