Question

1. Three people are selected at random from four females and seven males. Find the probability of the following. (See Example 4. Round your answers to three decimal places.)

- At least one is a male?
- At most two are male?

a) A tray of electronic components contains 23 components, 5 of which are defective. If 4 components are selected, what is the possibility of each of the following? (Round your answers to five decimal places.)

- that all 4 are defective?
- that 3 are defective and 1 is good?
- that exactly 2 are defective?
- that none are defective?

b) A person participates in a state lottery by selecting six numbers from 1 through 57. If the six numbers match the six drawn by the lottery, regardless of order, then the participant wins the first prize of millions of dollars. If a participant's numbers match five of the six drawn, the participant wins second prize, which is not millions of dollars.

- Find the probability of winning first prize. (Round your answer to ten decimal places)?
- Find the probability of winning second prize. (Round your answer to seven decimal places.)?

Answer #1

Q1. In a group of 40 children, 12 have blonde hair, 13 have
brown eyes, and 6 have both blonde hair and brown eyes. If a child
is selected at random, find the probability of the following.
(Round your answers to three decimal places.)
The child has blonde hair and brown eyes?
A) Three numbers are drawn from {1, 2, 3, 4, 5, 6, 7} and placed
in a row in the order drawn to form a three-digit number. What...

In the lottery game called 5/21, a player picks five numbers
from 1 to 21. Enter all answers as a decimal (not a percent),
rounded to five decimal places.
a) If all five of the numbers match the ones that are drawn, the
player wins first prize. What is the probability of winning this
prize?
b) If four of the five numbers match the ones that are drawn,
but the other number doesn't match, the player wins second prize.
What...

1) Suppose a jar contains 18 red marbles and 28 blue marbles. If
you reach in the jar and pull out 2 marbles at random, find the
probability that both are red.
Write your answer in decimal form, rounded to the nearest
thousandth.
2)In a certain state's lottery, 40 balls numbered 1 through 40
are placed in a machine and six of them are drawn at random. If the
six numbers drawn match the numbers that a player had chosen,...

In a certain state's lottery, 45 balls numbered 1 through 45 are
placed in a machine and seven of them are drawn at random. If the
seven numbers drawn match the numbers that a player had chosen, the
player wins $1,000,000. In this lottery, the order in which the
numbers are drawn does not matter.
Compute the probability that you win the million-dollar prize if
you purchase a single lottery ticket. Write your answer as a
reduced fraction.
PP(win) = ...

A lottery has a grand prize of $380,000, three runner-up prizes
of $76,000 each, seven third-place prizes of $9500 each, and
twenty-four consolation prizes of $760 each. If 760,000 tickets are
sold for $1 each and the probability of any one ticket winning is
the same as that of any other ticket winning, find the expected
return on a $1 ticket. (Round your answer to two decimal
places.)

The Florida lottery game Lotto is played by choosing six numbers
from 1 to 53. If these numbers match the ones drawn by the lottery
commission, you win the jackpot. The table below shows the
probability of winning a $32,000,000 jackpot, along with the
amounts and probabilities of other prizes. Assuming that the
jackpot was not split among multiple winners, find the expectation
for buying a $1 lottery ticket. Round to the nearest tenth of a
cent. (A calculator is...

1.a) Nine men and two women are semifinalists in a lottery. From
this group, seven finalists are to be selected by a drawing. What
is the probability that all seven finalists will be men? (Enter
your probability as a fraction.)
b) retailer purchases 240 of a new brand of DVD player, of which
4 are defective. The purchase agreement says that if he tests 5
chosen at random and finds 1 or more defective, he receives all the
DVD players...

1）To win a particular lottery, your ticket must match 6 different
numbers from 1 to 50, without regard to order.
a) How many combinations are possible?
2）To win a particular lottery,
your ticket must match 6 different numbers from 1 to 50, without
regard to order.
b) To win second
prize, 5 of the 6 winning numbers must match. How many outcomes are
possible for 2nd prize?
3）A NHL committee is being formed to look into
the effect of concussions...

7-If you select one card from a 52-card deck, find the
probability it is greater than 3 and less than 8.
8. Six movies (A, B, C, D, E, F) are being shown in random order.
Find the probability that B will be
shown first, F second, and D last.
9. In a lottery, six different numbers from 1-30 are drawn. A
player buys 1000 lottery tickets, all with
different sets of numbers. What is the probability this player wins...

Part 1
Armadillos are among the most common of Florida’s roadkill
victims. A study done along the Ronald Reagan Turnpike in central
Florida found an average of 1.9 armadillo roadkills per 100 miles
during the winter, when armadillos are least active [Source: M.
Inbar and R. T. Mayer, “Spatio-temporal trends in armadillo diurnal
activity and road-kills in central Florida,” Wildlife Society
Bulletin 27, no. 3 (1999).]
It’s New Year’s Day, and you and your friends are on a road trip...

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