e$)(2$ points$)$ What is P $[$E$]?$

$4.$ You have just created India$$s first AI language model ChaatGPT after intensive training on a corpus of Indian food data. In response to the prompt $$Suggest some tasty Indian food to eat today$,$ the model$$s output is the string:

$$ nothing $($i$.$e$.,$ the empty string $)$ with probability $0\mathrm{.}1$dahi$$ with probability $0\mathrm{.}2$

$$dahipuri$$ with probability $0\mathrm{.}15$

$$samosa$$ with probability $0\mathrm{.}3$

$$samosachaat$$ with probability $0\mathrm{.}2$

$$dahisamosachaat$$ with probability $0\mathrm{.}05$

$($a$)(2$ points$)$ Given that the model$$s output contains the st