Question

PROBLEM: Marbles in a Box Suppose there are 17 marbles in a box. There are 5 blue marbles, 4 yellow marbles, 3 red marbles, and 5 green marbles. The experiment is selecting 2 marbles randomly from the box, without replacement. Let x be the number of blue marbles. Note: The picture shown is an example of marbles in the box. The number of marbles and their color code does not reflect to this problem (a) Determine whether the experiment is a binomial experiment. Explain your reasoning If the experiment is a binomial experiment, proceed to the rest of the questions Otherwise, omit the rest of the questions (b) Calculate the mean, variance, and expected value. (c) Complete the following table. Let x be a random variable that represent the number of blue marbles drawn from the box. When necessary, round the probability to 4 significant digits (i.e. 0.1234), or use scientific notation. Binomial Formula & Calculator Command Probability X 1 2 4 5 O LO

Answer 1

Lel- there are 17 maubale in a box. out of which 5 blue marbles. 4. Yellow marbles 3 rued marbles 5 green mables. 2 mauebles Selected randomly fewom the box without geplacement. so, all possible oul- come, (17 (1) ways € 272 Now, hel- ees ole fine tee random vawwable X = Number of blue marble

Now, let us consider the selection of Blue marble as success and election of other marible as failure. as n=17 is quite large. So the distribution of Sandom variable x is a Binomial, with succees puusabilily 50 xu Binomial (17, 2). Now, x takes the value 0,1,2. X10 11 12 PCMCO 069 60 272 x 1 0 1 1 2 20 272 So, E(X) = Ox 432 tomt 42 x zaz z 0.367 ECX) 2 0 x 4 + 4x242 0.514 so, Varcx), E(X) - 64(x) = 0.574-135 a 0° 38

Binoryal formula, Puobability 0.003 0.019 0.06 (0) (33" (3) " (3) (4) 5) (3) 9 (57) 0113 . bino . 68100