1 A roulette wheel has 38 slots 2 of which are green 18 are

1. A roulette wheel has 38 slots, 2 of which are green, 18 are red, and 18 are black. A successful bet on black or red doubles the money, whereas one on green fetches 30 times as much. If you play the game once by betting $5 on the black, what are the probabilities that:

(a) You will lose your $5?

(b) You will win $5 or more?

(Give your answer as a fraction.)

2. A first step toward identifying spam is to create a list of words that are more likely to appear in spam than in normal messages. For instance, there are words like buy or the brand name of an enhancement drug that are more likely to occur in spam messages than in normal messages. Suppose a specified list of words is available and that your database of 1000 messages contains 350 that are spam.
Among the spam messages, 310 contain words in the list. Of the 650 normal messages, only 70 contain words in the list.

Obtain the probability that a message is spam given that the message contains certain words.

Solution