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• Unless otherwise specified, you can leave your answer in closed form (e.g. 1 – (120)(0.1)200).

• Show your work. Answers without justification will be given little credit. Justify each step in your

solutions e.g. by stating that the step follows from an axiom of probability, a definition, algebra, etc.;

for example, your answer could include a line like this:

Pr(XnYn Z) · Pr(AUB) = Pr(XnYN Z) · (Pr(A) + Pr(B)) (A and B are disjoint)

PROBLEM 1 (Experiments and events). Random Census, Inc. – a data science company – conducted a

study of families that have 1, 2, or 3 children, all having different ages (i.e., no family surveyed had twins).

The data scientists randomly sampled families and, for each sampled family, they wrote down the genders

of the children in ascending order, e.g., the outcome GB indicates that the family has two children, the

younger child is a girl, and the older child is a boy. They performed a statistical analysis of the data and

concluded that every possible configuration of genders and numbers of children is equally likely.

(a) Write down the sample space of this experiment and the probability of each outcome.

(b) For each of the following events, write down the set of outcomes comprising the event and find the

probability of the event.

A = “families where the youngest child is a girl”

B = “families with exactly two boys and any number of girls”

C = “families with at least one child of each gender”

Solution: Your solution here.

PROBLEM 2 (Deck of cards). We shuffle a standard deck of cards so that each permutation of the cards is

equally likely. Find the probability that the first card in the shuffled deck is:

(a) The Queen of diamonds (Q0).

(b) A heart or a diamond card.

(c) Not a face card, i.e., not Jack, Queen, or King.

Solution: Your solution here.

PROBLEM 3. In a special game of Pokemon Go, Alice must choose exactly two out of three pokemons:

Pikachu, Eeve, and Mewtwo. Alice chooses Mewtwo with probability 5/8, Pikachu with probability 5/8,

and Mewtwo and Pikachu together with probability 1/4.

(a) What is the probability that Alice chooses Eeve?

(b) What is the probability that Alice chooses Mewtwo or Pikachu?

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Explanation & Answer:

3 Problems

Tags:

algebra

probability

mathematics

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