math

Assume that the business makes a profit with probability 0.3 in the first year. For each year thereafter, the business makes a profit with probability 0.7 if it made a profit in the previous year, and with probability 0.2 if it did not make a profit in the previous year.

What is the probability that the business makes a profit in exactly two of its first three years?

  1. 👍 0
  2. 👎 2
  3. 👁 927
  1. make a tree where end endpoint has two branches coming off it
    Call one branch P for profit, the other branch NP for non-profit.
    The first year has 2 endpoints, the 2nd year has 4 endpoints, and the 3rd year has 8 endpoints.

    Place the appropriate P at the end of each branch, and write the probability on each branch

    prob of profit in 1st year = .3

    pathways to get to P in year two
    = (.7)(.3) + (.7)(.2) = .35
    pathways to get to P in year 3
    = (.7^2)(.3) + (.3^2)(.2) + (.7^2)(.2) + (.7)(.8)(.2) = .375

    so to have 2 out of the 3 years it could be years
    1,2 or 1,3 or 2,3

    prob = (.3)(.35) + (.3)(.375) + (.35)(.375) = .34875

    Check my calculations, this was a tricky question.
    I did all up all the P and NP prob in year 3 and they added to 1 as they should

    1. 👍 0
    2. 👎 1

Respond to this Question

First Name

Your Response

Similar Questions

  1. Probability

    Sophia is vacationing in Monte Carlo. On any given night, she takes X dollars to the casino and returns with Y dollars. The random variable X has the PDF shown in the figure. Conditional on X=x , the continuous random variable Y

  2. Personal Finance

    Check my work pls. 1. The components of ___ are variable costs and fixed costs. A. Entire cost B. Total cost* C. Complete cost D. Required cost 2. What is the margin of safety? A. How much sales can fall before a business starts

  3. Statistics

    An investor is considering an investment in a start-up company. she estimates that she has probability 0.25 of a $ 39,739 loss, probability 0.20 of a $ 19,759 profit, probability 0.15 of a $ 49,068 profit, and probability 0.40 of

  4. maths

    1. a man sells a tv for rupees 3450and makes a profit of 15% . he sells a second tv set at a loss of 10%.if on the whole he neither gains nor loses , find the cost price of the second tv. 2.a man sells two tables at the same

  1. math

    A contractor is considering a sale that promises a profit of $ 26,000 with a probability of .7 or a loss (due to bad weather, strikes, and such) of $ 4000 with a probability of .3. What is the expected profit. Can someone help me

  2. math

    A new computer software company earns a profit of $245 000 in its first year. The company expects the profit to increase by 15% each year for each subsequent year. (a) What profit can the company expect to earn in its seventh

  3. Finance

    Personal Finance school can you check my answers? 1. The two components of are variable costs and fixed costs. Entire cost Total cost* Complete cost Required cost 2. What is the margin of safety? How much sales can fall before a

  4. math for the office professional

    last year the company you worked for did $232,000 in business. this year you anticipate an increase of 7% how much business do you expect to do this year?

  1. Math

    2. Lisa owns a small business. There was a loss of $14 on Monday and a profit of $18 on Tuesday. On Wednesday there was a loss of $6 and on Thursday there was a profit of $7. Find the total profit or loss. a. $15 profit b. $45

  2. Managerial Economics Question

    1)The Midnight hour, a local nightclub, earned $100,000 in accounting profit last year. This year the owner, who had invested $ 1 million in the club, decided to close the club. What can you say about economic profit (and the rate

  3. Math (Ms.Sue please help!)

    Sarah owns a small business. There was a loss of $19 on Thursday and a loss of $12 on Friday. On Saturday there was a loss of $11, and on Sunday there was a profit of $15. Find the total profit or loss for the four days. A. $35

  4. Economics

    I got a lot of problems with this exercise. I really hope you can help me. Thanks! Samantha Roberts has a job as a pharmacist earning $30.000 per year, and she is deciding whether to take another job as the manager of another

You can view more similar questions or ask a new question.