Answers for 7 & 8 , conditional probabilities- geometry module 6 version 2

7) I'm assuming any pizza comes with cheese by default and that it shouldn't technically count as a topping on its own. It's probably safe to also assume that a pizza with sausage and pepperoni, for instance, is the same as a pizza with pepperoni and sausage, i.e. the order of toppings does not matter.

Then the number of pizzas that can be made with no more than 5 toppings would be

8) Let be the random variable representing the earning/loss after drawing a bead. has the probability mass function

The expected value for any given draw is

The game would be fair if the expectation was $0, but this one is actually in favor of the player.

goog may have it for you