In a large bag of marbles 35 of them are red A child chooses

In a large bag of marbles, 35% of them are red. A child chooses 4 marbles from this bag. If the child chooses the marbles at random, what is the chance that the child gets exactly three red marbles? Use the binomial formula and show all work.

Solution

Note that the probability of x successes out of n trials is          
          
P(n, x) = nCx p^x (1 - p)^(n - x)          
          
where          
          
n = number of trials =    4      
p = the probability of a success =    0.35      
x = the number of successes =    3      
          
Thus, the probability is          
          
P (    3   ) =    0.111475 [answer]