QUESTION $19$

$4\mathrm{.}76(4\mathrm{.}92)($a$)$ Choose between two public health programs that $$ffect $600$ people. $[$Program $1]$ has probability $\frac{1}{2}$ of saving all $600$ and probability $\frac{1}{2}$ that all $600$ will die. The other $[$Program $2]$ is guaranteed to save exactly $400$ of the $600$ people. Find the mean number of people saved in each program.

Program $1$: $300$; Program $2$: $200$

Program $1$: $300$ ; Program $2$: $400$

Program $1$: $300$ ; Program $2$: $300$