Let Bernoulli random variable $J_i$ indicate whether jock $i$ gets accepted for $i \in {1,2,...,12}$ (meaning $$J_i = 1$$ if $i$ is accepted, 0 otherwise). Let Bernoulli random variable $G_j$ indicate whether goth $j$ gets accepted for $j \in {1,2,3,4}$. Applying linearity of expectation,

$$E\Big[\sum_{i=1}^{12} J_i + \sum_{j=1}^{4} G_j \Big] = \sum_{i=1}^{12} E[J_i] + \sum_{j=1}^{4} E[G_j] = \sum_{i=1}^{12} 0.1 + \sum_{j=1}^{4} 0.2 = 2$$

Because all random variables are independent, we can break apart the variance without covariance terms,

$$V\Big[\sum_{i=1}^{12} J_i + \sum_{j=1}^{4} G_j \Big] = \sum_{i=1}^{12} V[J_i] + \sum_{j=1}^{4} V[G_j] = \sum_{i=1}^{12} (0.1)(1-0.1) + \sum_{j=1}^{4} (0.2)(1-0.2) = 1.72$$