a. x~bin(20,0.25)
b. µ = np = 20*0.25 = 5
c. P[20] = 0.25^20 = 9.0949e-13
d. P[≥10] = 0.0139 or 1.39%
so 10 guesses correct is unlikely by chance, but not that unlikely that i'd belirve that the force is with him !
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 that 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?
c) What is the probability that Anakin guesses all 20 cards correctly?
d) Suppose Anakin guesses correctly on 10 of the cards. What is the probability of him doing this well or better by chance? Do you think he has the force with him?
1 answer
1 answer