Answer
$P(x < 5) = 0.0949$
Work Step by Step
The probability of getting $x$ successes in a binomial experiment is given by: ${n}\choose{x}$ $\cdot$ $p^xq^{n-x}$
$P(x < 5) = P(0) + P(1) + P(2) + P(3) + P(4)$
P(0) = ${10}\choose{0}$ $\cdot$ $0.65^00.35^{10-0} \approx 0$
P(1) = ${10}\choose{1}$ $\cdot$ $0.65^10.35^{10-1}$ = 0.0005
P(2) = ${10}\choose{2}$ $\cdot$ $0.65^20.35^{10-2}$ = 0.0043
P(3) = ${10}\choose{3}$ $\cdot$ $0.65^30.35^{10-3}$ = 0.0212
P(4) = ${10}\choose{4}$ $\cdot$ $0.65^40.35^{10-4}$ = 0.0689
Therefore $P(x < 5) = 0 + 0.0005 + 0.0043 + 0.0212 + 0.0689 = 0.0949$
