Question 1177793
(a) {{{P(x = r)= highlight_green(400Cr)(.03^r)(.97)^(400-r) }}} 
(b) P(x ≥ k) = 1 - P(x ≤ (k-1)) = 1 -  {{{highlight_green(400C(k-1))(.03^(k-1))(.97)^(n-(k-1)) }}}
(c) P(x ≤ 1) = binomcdf(400, .03, 1) = .00006
or
  P(x=0) + P(x=1)
(c)  Expected value .03*400 = 12
 in (a) as r approaches 12,  P gets larger.  In (b) P gets smaller
in (c) the probability is small because x ≤ 1 is so much less that expected value of 12.