Quiz to be completed

( MATH106 Quiz-5 )

Covers material from sections 8.1, 8.2, 8.3, 8.5

( 1 )(0.5 points) Section 8.1

In a family with 3 children, what is the probability of having 2 boys and 1 girls, assuming that a boy is as likely as a girl at each birth? Consider two cases: A) 2 boys and 1 girl were born in that order. B) 2 boys and 1 girl were born in any order. Tip: construct sample space for all possible events, count how many outcomes related to case A and case B. To obtain probability, divide by number of all possible outcomes.

( 2 )(1 point) Section 8.1 Suppose 20 candidates, 10 male and 10 female, apply for 5 vacant positions. If positions were filled randomly, what is the probability that it’ll be 3 male and 2 female?

( 3 )(0.5 points) Section 8.2 What is the probability and what are the odds in favor of the following event: a card drawn from the full standard 52-card deck will be a Queen or any card of a Heart? Don’t forget: one card is Queen and Heart, so P(Queen ⋂ Heart) = 1/52

( 4 ) ( 4 )(0.5 points) Section 8.2 Venn diagram shows number of elements in each sector:

( A B 33 12 25 10 )

Keep in mind, 25 elements from A do not include 10 elements from A⋂B and 12 elements from B do not include 10 elements from A⋂B. 33 shows us the number of element only in white section.

Based on this diagram, find Probability that element belongs to not A: P(A’)

( 5 ) ( 5 )(1 point) Section 8.3 Use probabilities from table below

	B	D
A	0.12	0.28
C	0.38	0.22

and formula for conditional probability on page 399: to find following probabilities: P(A|B), P(D|C).

( 6 ) ( 6 )(1 point) Section 8.3

A box contains 2 red, 4 white and 6 green balls. Two balls are drawn without replacement (first taken ball is not returned back to the box). What is the probability that both taken balls will have the same color (both red or both white or both green)?

( 7 )(0.5 points) Section 8.5

Calculate Expected Value for the following Discrete Probability Distribution:

x	-1	0	1	2	3
P(x)	0.08	0.11	0.22	0.26	0.33

( 8 )(1 point) Section 8.5

A card is drawn from a standard 52-card deck. If the card is a diamond, you win $5; otherwise, you lose $1. What is the expected value of this game? Who wins on a long run: you or the house?