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1. Let P be a probability and let A; B; C be any events. Then:
2. Let P be a probability and let A and B be two independent events. Then:
3. Let P be a probability and let A and B be two events. If the random
variable X is defined by X = 1A + 2 1B then
4. In a class, 60% of students have an Apple account, 50% have a Google+
Account and 30% have both.
(a) How many (in percentage) don’t have either?
(b) How many (in percentage) have and Apple account but not a Google+
account?
5. In how many different ways 5 people can sleep in a house with 3 rooms
(one person per room and only 3 people can sleep in the house) ?
6. How many different committees of 3 members can be formed out of a
group of 7 people.
7. Suppose a class contains 60% girls and 40% boys. Suppose that 20% of
the girls have blue eyes and 10 % of the boys have blue eyes. What is the
probability that a randomly chosen student has blue eyes ?
8. Suppose that: the probability of snow is 20%, the probability of traffic
accident is 10%, the conditional probability of an accident given that it
snows is 40%. What is the conditional probability that it snow given that
there is an accident?
9. You flip 8 fair coins. Count the number of sequences with exactly 3 Tails.
10. Write the definition of the variance of a random variable and 3 of its
properties.
11. Let P be a probability and let A be any event in the sample space. Prove
that: P (AC ) = 1 P (A):
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