Mary will be taking a 20-question, multiple-choice exam with three choices for each question. She has another important project to be submitted on the same day. If Mary guesses on each question of the exam, find the probability of guessing exactly 8 out of 20 correctly.
Use the excerpt The Zimmerman Telegram, 1917 to answer the question.
What was Germany's purpose in sending the telegram? Explain
A. to propose an alliance with Mexico against the United States
B. to convince Mexico to become involved in the First World War
C. to demonstrate to the United States that it was surrounded by enemies
D. to create a situation in which Mexico was forced to surrender its colonies
A. to propose an alliance with Mexico against the United States.
Use the excerpt The Zimmerman Telegram, 1917 to answer the question.
What was Germany's purpose in sending the telegram? EXPLAIN YOUR ANSWER
A. to propose an alliance with Mexico against the United States
B. to convince Mexico to become involved in the First World War
C. to demonstrate to the United States that it was surrounded by enemies
D. to create a situation in which Mexico was forced to surrender its colonies
The purpose of Germany in sending the Zimmerman telegram was to propose an alliance with Mexico against the United States. The telegram stated that if Mexico joined the war on Germany's side, they will receive financial support, and in return, they needed to attack the United States. The main intention of Germany was to create chaos in North America, and keep the United States occupied with the attack from Mexico, so that Germany could focus on the war in Europe. Therefore, option A is the correct answer.
To find the probability of guessing exactly 8 out of 20 correctly, we need to use the concept of probability and the binomial probability formula.
The binomial probability formula is given by:
P(X = k) = C(n,k) * p^k * (1-p)^(n-k)
Where:
P(X = k) is the probability of getting exactly k successes
C(n,k) is the combination formula (n choose k)
p is the probability of success on a single trial
n is the total number of trials
In this case, Mary has 20 questions, and she has a 1/3 probability of guessing the answer correctly for each question. Therefore, p = 1/3 and n = 20.
Now let's calculate the probability of guessing exactly 8 out of 20 correctly using the formula.
P(X = 8) = C(20, 8) * (1/3)^8 * (2/3)^(20-8)
To calculate C(20, 8), use the combination formula:
C(20, 8) = 20! / (8! * (20-8)!)
Now, let's substitute the values and calculate the final probability:
C(20, 8) = 20! / (8! * (20-8)!)
= 20! / (8! * 12!)
= (20*19*18*17*16*15*14*13) / (8*7*6*5*4*3*2*1)
Using a calculator or any appropriate tool, evaluate C(20, 8):
C(20, 8) = 125,970
Substituting this value into the binomial formula:
P(X = 8) = 125,970 * (1/3)^8 * (2/3)^(20-8)
Evaluate (1/3)^8 and (2/3)^(20-8) using a calculator:
(1/3)^8 = 0.000002
(2/3)^(20-8) = 0.0000000463
Now, multiply these values by 125,970:
P(X = 8) = 125,970 * 0.000002 * 0.0000000463
Evaluate this expression:
P(X = 8) = 0.000002895
Therefore, the probability of guessing exactly 8 out of 20 correctly is approximately 0.000002895.
prob(correct) = 1/3
prob(wrong) = 2/3
prob(exactly 8 of 20 correct) = C(20,8) (1/3)^8 (2/3)^12
= appr ......