A lottery is conducted in which 7 winning numbers are randomly selected from a total of 62 numbers (1-62). In addition, the Powerball, a single winning number, is selected from an independent pool of 26 numbers (1-26). You select 7 numbers from the pool of 62 numbers.

If the probability of choosing 2 of the 7 winning numbers from the pool of 62 numbers is .08862, what is the probability will choose the Powerball from the pool of 26 numbers?

A manufacturing company prepares a box of 25 items for shipment, and a random sample of 3
items is selected and tested for defectives. If any defectives are found, the entire box is sent
back for 100% screening; if no defectives are found, the box is shipped.

What is the distribution of the number of defective items found in the random
sample? (I think it is NegBin)

What is the probability that a box containing 3 defectives will be shipped?

What is the probability that a box containing 1 defective will be sent back for
screening?

In our rental shop case, we know that on the busiest day we can expect 150 rentals, which forms the number of independent events or trials. We also know that, historically, 60% of our customers rent skis and 40% rent snowboards, which provides our probability. If we decide that we only need to have 65 snowboards in stock, what is the probability that we will run out of snowboard rentals on any specific day?

According to an​ article, 47​% of adults have experienced a breakup at least once during the last 10 years. Of 9 randomly selected​ adults, find the probability that the​ number, X, who have experienced a breakup at least once during the last 10 years is

a. exactly​ five; at most​ five; at least five.

b. at least​ one; at most one.

c. between five and seven​, inclusive.

d. Determine the probability distribution of the random variable X.

a.) Suppose that government data show that 8% of adults are full‑time college students and that 30% of adults are age 55 or older. Complete the passage describing the relationship between the two aforementioned events. Although (0.08)⋅(0.30)=0.024, we cannot conclude that 2.4% of adults are college students 55 or older because the two events __________(are/are not) ________(independent/disjoint)

b.) In New York State's Quick Draw lottery, players choose between one and ten numbers that range from 11 to 80.80. A total of 2020winning numbers are randomly selected and displayed on a screen. If you choose a single number, your probability of selecting a winning number is 2080,2080, or 0.25.0.25. Suppose Lester plays the Quick Draw lottery 66 times. Each time, Lester only chooses a single number.

What is the probability that he loses all 66 of his lottery games? Please give your answer to three decimal places.

c.) Consider the sample space of all people living in the United States, and within that sample space, the following two events.

??=people who play tennis=people who are left‑handedA=people who play tennisB=people who are left‑handed

Suppose the following statements describe probabilities regarding these two events. Which of the statements describe conditional probabilities? Select all that apply:

-Two‑tenths of a percent of people living in the United States are left‑handed tennis players.

-Two percent of left‑handed people play tennis.

-Of people living in the United States, 3.7% play tennis.

-There is a 10.2% chance that a randomly chosen person is left‑handed.

-The probability is 5.4% that a tennis player is left‑handed.

-There is a 13.7% probability that a person is a tennis player or left‑handed.

d.)

Of all college degrees awarded in the United States, 50%50% are bachelor's degrees, 59%59% are earned by women, and 29%29% are bachelor's degrees earned by women. Let ?(?)P(B) represent the probability that a randomly selected college degree is a bachelor's degree, and let ?(?)P(W) represent the probability that a randomly selected college degree was earned by a woman.

What is the conditional probability that a degree is earned by a woman, given that the degree is a bachelor's degree? Please round your answer to the two decimal places.

Program 5: Decimal to Binary

In Computer Science we often work with different number systems to represent data. The most commonly used number system (which we refer to as "decimal") is a "base 10" number system, which means that we use the values 0-9 to represent all numbers.

The binary number system is a "base 2" number system, which means that we use the values 0 and 1 to represent all numbers. We refer to each value in a binary number as a "bit" (i.e. the number 0101 consists of 4 bits). Here are some numbers represented in both base 10 and base 2:

This is the algorithm for converting a decimal number into a binary number:

• Attempt to divide the number by 2.
• If there is a remainder you should record the bit 1.
• If there is no remainder, you should record the bit 0.
• Divide the number by 2 and throw away the remainder.
• If the number is positive, repeat the process.
• If the number is 0, you should end the process.

Note that each successive bit you compute is for the next highest place (the next highest power of 2) -- so it will be inserted at the front (or the left-end) of the binary number.

For example, consider the following decimal number:

decimal = 5

Here is how the algorithm works on this number:

    5 ÷ 2 = 2 remainder 1               Record this bit:    1
    5 // 2 = 2
    2 ÷ 2 = 1 remainder 0               Record this bit:   01
    2 // 2 = 1
    1 ÷ 2 = 0 remainder 1               Record this bit:  101
    1 // 2 = 0 (algorithm stops)

For this problem, write a program that prompts the user for an integer greater than or equal to zero. If the user supplies a value less than 0 you should re-prompt them. Then convert the number to binary, printing out each step in the process as you go.

Note: Your binary value can't be recorded as an integer. Since you are building the number up bit-by-bit, you will probably need to keep track of 0's that are in higher place values than the the highest 1 bit, in other words, leading zeros. Integers do not support leading 0's (i.e. 0001 will be reduced to 1). Therefore, for this program you should use a String to hold your bits (i.e. "0001" is allowed). You will need to figure out a way how to add bits to your String (hint: concatenation)

Here are a few sample runnings of your program:

Enter a number greater than or equal to 0: -5
Invalid, try again
Enter a number greater than or equal to 0: -9
Invalid, try again
Enter a number greater than or equal to 0: 9
9 % 2 = 1 ---> 1
9 // 2 = 4
4 % 2 = 0 ---> 01
4 // 2 = 2
2 % 2 = 0 ---> 001
2 // 2 = 1
1 % 2 = 1 ---> 1001
1 // 2 = 0

9 in binary is 1001

Enter a number greater than or equal to 0: 86
86 % 2 = 0 ---> 0
86 // 2 = 43
43 % 2 = 1 ---> 10
43 // 2 = 21
21 % 2 = 1 ---> 110
21 // 2 = 10
10 % 2 = 0 ---> 0110
10 // 2 = 5
5 % 2 = 1 ---> 10110
5 // 2 = 2
2 % 2 = 0 ---> 010110
2 // 2 = 1
1 % 2 = 1 ---> 1010110
1 // 2 = 0

86 in binary is 1010110

Enter a number greater than or equal to 0: 255
255 % 2 = 1 ---> 1
255 // 2 = 127
127 % 2 = 1 ---> 11
127 // 2 = 63
63 % 2 = 1 ---> 111
63 // 2 = 31
31 % 2 = 1 ---> 1111
31 // 2 = 15
15 % 2 = 1 ---> 11111
15 // 2 = 7
7 % 2 = 1 ---> 111111
7 // 2 = 3
3 % 2 = 1 ---> 1111111
3 // 2 = 1
1 % 2 = 1 ---> 11111111
1 // 2 = 0

255 in binary is 11111111

Enter a number greater than or equal to 0: 256
256 % 2 = 0 ---> 0
256 // 2 = 128
128 % 2 = 0 ---> 00
128 // 2 = 64
64 % 2 = 0 ---> 000
64 // 2 = 32
32 % 2 = 0 ---> 0000
32 // 2 = 16
16 % 2 = 0 ---> 00000
16 // 2 = 8
8 % 2 = 0 ---> 000000
8 // 2 = 4
4 % 2 = 0 ---> 0000000
4 // 2 = 2
2 % 2 = 0 ---> 00000000
2 // 2 = 1
1 % 2 = 1 ---> 100000000
1 // 2 = 0

256 in binary is 100000000

This program should be named as follows: LastNameFirstName_assign4_problem5.py (for example, "KappCraig_assign4_problem5.py")

Question 4.4

1. Give two examples of financial markets.
2. Identify the demanders and suppliers in a financial market.
3. Explain why interest rates are the price of lending or borrowing loanable funds. Show the equilibrium interest rate (r*) on a graph.
4. Explain what usury laws are, articulating who wins and who loses when a cap is placed on the amount of interest that could be charged in the financial markets. Graph this effect.

Neelo Mbiganyi received a notice of assessment from BURS and the Commissioner General had disallowed some of the expenditures that she had claimed. Discuss the appeals and objection processes that Neelo can follow explaining in detail the rights and obligations that both Neelo and the Commissioner General have in these processes. In your answer, also explain what the Commissioner General should do suppose Neelo wins the case

A town in California is broke. The city had been warned several times over the last few years that it did not have enough money to pay out future pensioners. There is a law that says the town must pay promised benefits. The town says that it cannot, no money. You be the judge. Who wins here? The town or the pensioners? Why did they win and what did you cite for the reasons?