Question

Part V. 1. Events G and H are defined on the sample space. If P(G) = 0.3, P(H) = 0.2, and P(G ! H) = 0.1 a) Are G and H independent? Explain. __________________________________________________________________________ b) Are G and H mutually exclusive? Explain. ___________________________________________________________________________ 2. The classical probability concept applies only when all possible outcomes are ______________________. 5 3. If A is the event that I win the lottery and B is the event that I go on vacation, then P(B | A) can be described in words as the probability that ______________________________________________________________. 4. A restaurant menu has 8 main courses, 5 appetizers, 6 desserts, and 4 beverages. The number of ways that a patron can select a meal with one appetizer, one main course, one dessert and one beverage is ________________________________________________. 5. The number of 5-player basketball teams that can be formed from a group of 11 players is _______________________________________________. 6. How many ways can letters of PROBABILITY be arranged? _____________________________________________.

Answer 1

Solution:

Question 1)

Given: Events G and H are defined on the sample space.

P(G) = 0.3, P(H) = 0.2, and P(G | H) = 0.1

Part a) Are G and H independent?

Events are independent if and only if:

P(A | B) = P(A)

We have P(G | H) = 0.1 and P(G) =0.3

Since P(G | H) = 0.1 which is not equal to P(G) =0.3

Thus event G and H are not independent.

Part b) Are G and H mutually exclusive? Explain.

Events are Mutually exclusive, if

P( A and B) = 0

We have
P(G|H) = 0.1 and P(H) =0.2

Using conditional probability formula:

That is: P( G and H) = 0.02 which is not 0

Hence events G and H are not mutually exclusive.

Question 2) The classical probability concept applies only when all possible outcomes are Equally likely.

( That is every unit in the sample space has an equal chance)

Question 3) If A is the event that I win the lottery and B is the event that I go on vacation,

then P(B | A) can be described in words as the probability that I go on vacation given that I win the lottery.

Question 4) A restaurant menu has 8 main courses, 5 appetizers, 6 desserts, and 4 beverages.

The number of ways that a patron can select a meal with one appetizer, one main course, one dessert and one beverage is :

one appetizer can be chosen from 5 appetizers in 5 ways

one main course can be chosen 8 main courses in 8 ways

one dessert can be chosen 6 dessert in 6 ways

one beverage can be chosen 4 beverage in 4 ways

Thus total ways = 5 x 8 x 6 x 4 = 960 ways.

Question 5) The number of 5-player basketball teams that can be formed from a group of 11 players is

Using combination formula:

5 players chosen from 11 players has ₁₁C₅ ways

Question 6) How many ways can letters of PROBABILITY be arranged?

PROBABILITY has 11 letters

Thus n = 11

n1 = B is two times = 2

n2 = I is two times = 2

and other letters are occurred once.

Thus

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