Questions (a) and (b) require the formula for cumulative probability for a geometric distribution. See

Geometric distribution - Wikipedia, the free encyclopedia:

$\displaystyle \Pr(X \leq k) = 1 - (1 - p)^k$.

(a) Substitute p = 0.1 and k = 10.

(b) $\displaystyle = \Pr(X \leq 10) - \Pr(X \leq {\color{red}4})$. Calculate each of these just like (a) but use p = 0.2.

(c) Poisson distribution with a mean of 5: $\displaystyle \lambda = 5$. You need to substitute into the probability mass function (pmf). See

Poisson distribution - Wikipedia, the free encyclopedia:

$\displaystyle \Pr(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}$.

Substitute $\displaystyle \lambda = 5$ and k = 0. Then do the same for k = 1, 2, 3, 4, 5. Then add up all these probabilities to get the answer.