An exceptionally bright high school student has applied for two scholarships: a merit scholarship and an athletic scholarship. He estimates the following probabilities: The probability of getting the merit scholarship is 0.3 The probability of getting the athletic scholarship is 0.6 The probability of getting both scholarships is 0.08. (a) What is the probability that he does not get the merit scholarship? (b) What is the probability that he gets at least one of these scholarships?

1 answer
Question:

An exceptionally bright high school student has applied for two scholarships: a merit scholarship and an athletic scholarship. He estimates the following probabilities: The probability of getting the merit scholarship is 0.3 The probability of getting the athletic scholarship is 0.6 The probability of getting both scholarships is 0.08.
(a) What is the probability that he does not get the merit scholarship?
(b) What is the probability that he gets at least one of these scholarships?

Answers

Answer:a) 0.70b) 0.82Step-by-step explanation:a)Let M be the event that student get merit scholarship and A be the event that student get athletic scholarship.P(M)=0.3P(A)=0.6P(M∩A)=0.08P(not getting merit scholarships)=P(M')=?P(not getting merit scholarships)=1-P(M)P(not getting merit scholarships)=1-0.3P(not getting merit scholarships)=0.7The probability that student not get the merit scholarship is 70%.b)P(getting at least one of two scholarships)=P(M or A)=P(M∪A)P(getting at least one of two scholarships)=P(M)+P(A)-P(M∩A)P(getting at least one of two scholarships)=0.3+0.6-0.08P(getting at least one of two scholarships)=0.9-0.08P(getting at least one of two scholarships)=0.82The probability that student gets at least one of two scholarships is 82%.

Similar Solved Questions

2 answers

Using the letters in the word ADDITION, find the number of permutations that can be formed using 3 letters at a time.

Using the letters in the word ADDITION, find the number of permutations that can be formed using 3 letters at a time....
1 answer

Which of the following was not a term from the Treaty of Versailles: a) German army limited to 100,000 b) Germany to pay $5 billion in reparations c) Germany to have no submarines d) Germany to write letters of apology to all victims.

Which of the following was not a term from the Treaty of Versailles: a) German army limited to 100,000 b) Germany to pay $5 billion in reparations c) Germany to have no submarines d) Germany to write letters of apology to all victims....
1 answer

The world record for the most number of push-ups in 60 seconds is 140 push-ups. If the record holder completed the push-ups at a constant ratio of seconds to push-ups, how many push-ups did he complete in 45 seconds?

The world record for the most number of push-ups in 60 seconds is 140 push-ups. If the record holder completed the push-ups at a constant ratio of seconds to push-ups, how many push-ups did he complete in 45 seconds?...
1 answer

Why are agricultural products hard to grow in northern Alaska?

Why are agricultural products hard to grow in northern Alaska?...
2 answers

Draw in radii OK and NL. Since OK and JK are radii of the same circle, they are _________. This means that OK = 12. Add the length of OK to the diagram.

Draw in radii OK and NL. Since OK and JK are radii of the same circle, they are _________. This means that OK = 12. Add the length of OK to the diagram....
1 answer

Cos3A-sin3A/1-2sin2A= cosA + sinA. Prove the identity ​

cos3A-sin3A/1-2sin2A= cosA + sinA. Prove the identity ​...
2 answers

An apple has 6 J of energy. The apple sits on a counter 3 m high. What is the mass of the apple?

An apple has 6 J of energy. The apple sits on a counter 3 m high. What is the mass of the apple?...
1 answer

Where is the image located when an objectis placed 30cm from a convex lens with a focal length of 10cm?​

where is the image located when an objectis placed 30cm from a convex lens with a focal length of 10cm?​...
2 answers

What is the name for subatomic particle in an atom that has no charge

What is the name for subatomic particle in an atom that has no charge...
1 answer

1 Which literary genre features characters and settings that resemble real life?

1 Which literary genre features characters and settings that resemble real life?...
1 answer

The balance in allowance for doubtful accounts will directly impact the end-of-period adjustment for bad debt expense when using the a. declining value method b. accrual method c. allowance method based on aging the receivables d. direct write-off method

The balance in allowance for doubtful accounts will directly impact the end-of-period adjustment for bad debt expense when using the a. declining value method b. accrual method c. allowance method based on aging the receivables d. direct write-off method...
1 answer

Ury Studies (4th 9 Weeks Spring 2020) Checking for Understanding Match each term with its correct definition or description ideology beliefs that state how a group believes society should work balance of power when no one state is more powerful than others 0 bogve up the go to take to give up the right to rule abdicate a sudden, often violent overthrow of a government

ury Studies (4th 9 Weeks Spring 2020) Checking for Understanding Match each term with its correct definition or description ideology beliefs that state how a group believes society should work balance of power when no one state is more powerful than others 0 bogve up the go to take to give up the ri...
1 answer

Dafydd bought a bike for £300 on 1st February 2010. Every year the value of the bike depreciates by 18% of its' value at the start of the year. Find the value of the bike on 1st February 2014.

Dafydd bought a bike for £300 on 1st February 2010. Every year the value of the bike depreciates by 18% of its' value at the start of the year. Find the value of the bike on 1st February 2014....
1 answer

Veterinária Porque a atuação dos hormônios e lenta em comparação com o sistema nervoso?

Veterinária Porque a atuação dos hormônios e lenta em comparação com o sistema nervoso?...
2 answers

Which of the following best describes William Penn's vision for living in America? He plotted to change the customs and religion of the Native Americans. He wanted to practice ideals such as religious freedom and toleration. He envisioned building large cities where his people could become wealthy. He planned for his people to fight the Native Americans and take over their land.

Which of the following best describes William Penn's vision for living in America? He plotted to change the customs and religion of the Native Americans. He wanted to practice ideals such as religious freedom and toleration. He envisioned building large cities where his people could become wealthy. ...
1 answer

Soul music during the 1960s was characterized by . . . A) high, soaring vocals. B) highly decorated, emotional vocal techniques. C) call and response between the lead singer and backup singers. D) smooth, choreographed dance movements. E) All of the above

Soul music during the 1960s was characterized by . . . A) high, soaring vocals. B) highly decorated, emotional vocal techniques. C) call and response between the lead singer and backup singers. D) smooth, choreographed dance movements. E) All of the above...
1 answer

4. Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours. How many miles does he need to drive each hour?

4. Brian is driving 324 miles to visit some friends. He wants to get there in 6 hours. How many miles does he need to drive each hour?...
1 answer

Who were the "Hollywood Ten," and what happened to them?

Who were the "Hollywood Ten," and what happened to them?...

-- 0.053185--