Some people believe in the force (yes, like in Star Wars). To test if young Anakin Skywalker has the force with him, he is told that some cards the Yoda can see but Anakin cannot contain a picture of a planet, a lightsaber, a laser rifle, or a spaceship. As Yoda looks at 20 such cards in turn, Anakin tries to guess what is on the card Yoda is looking at. Of course, Anakin has a 25% chance of simply guessing correctly.
a) Verify that the count of correct guesses in 20 cards follows a binomial distribution and write the notation.
b) What is the mean number of correct guesses?

Question

Some people believe in the force (yes, like in Star Wars). To test if young Anakin Skywalker has the force with him, he is told that some cards the Yoda can see but Anakin cannot contain a picture of a planet, a lightsaber, a laser rifle, or a spaceship. As Yoda looks at 20 such cards in turn, Anakin tries to guess what is on the card Yoda is looking at. Of course, Anakin has a 25% chance of simply guessing correctly. 
a)	Verify that the count of correct guesses in 20 cards follows a binomial distribution and write the notation.
b)	What is the mean number of correct guesses?