Three students

Three students independently try to solve the problem. The first student will solve a similar problem with a probability of 0.6, the second student will solve at a probability of 0.55, and the third will solve at a probability 0.04. The problem is resolved, What is the probability that the first student has solved it?

Result

p =  0.496

Solution:

$p_{ 1 } = 0.6 + 0.55 - 0.6 \cdot \ 0.55 = 0.82 \ \\ p_{ 2 } = p_{ 1 } + 0.04 - p_{ 1 } \cdot \ 0.04 = 0.82 + 0.04 - 0.82 \cdot \ 0.04 = \dfrac{ 517 }{ 625 } = 0.8272 \ \\ \ \\ p = 0.6 \cdot \ p_{ 2 } = 0.6 \cdot \ 0.8272 \doteq 0.4963 = 0.496$

Try another example

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 0 comments:

Be the first to comment!

Next similar math problems:

1. Three shooters
   Three shooters shoot, each one time, on the same target. The first hit the target with a probability of 0.7; second with a probability of 0.8 and a third with a probability of 0.9. What is the probability to hit the target: a) just once b) at least once
2. Cards
   Suppose that are three cards in the hats. One is red on both sides, one of which is black on both sides, and a third one side red and the second black. We are pulled out of a hat randomly one card and we see that one side of it is red. What is the probab
3. A pizza
   A pizza place offers 14 different toppings. How many different three topping pizzas can you order?
4. Candies
   In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ?
5. Theorem prove
   We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
6. Trinity
   How many different triads can be selected from the group 43 students?
7. Test
   The teacher prepared a test with ten questions. The student has the option to choose one correct answer from the four (A, B, C, D). The student did not get a written exam at all. What is the probability that: a) He answers half correctly. b) He answers
8. Shooters
   In army regiment are six shooters. The first shooter target hit with a probability of 49%, next with 75%, 41%, 20%, 34%, 63%. Calculate the probability of target hit when shooting all at once.
9. One green
   In the container are 45 white and 15 balls. We randomly select 5 balls. What is the probability that it will be a maximum one green?
10. A book
    A book contains 524 pages. If it is known that a person will select any one page between the pages numbered 125 and 384, find the probability of choosing the page numbered 252 or 253.
11. Cards
    The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
12. Balls
    We have n identical balls (numbered 1-n) is selected without replacement. Determine 1) The probability that at least one tensile strength number coincides with the number of balls? 2) Determine the mean and variance of the number of balls, which coincides.
13. Family
    What is the probability that a family with 7 childrens have: exactly 5 girls? 7 girls and 0 boys? Consider the birth probability of a girl is 48.69% and boy 51.31%.
14. Genetic disease
    One genetic disease was tested positive in both parents of one family. It has been known that any child in this family has a 25% risk of inheriting the disease. A family has 3 children. What is the probability of this family having one child who inherited
15. Probability of malaria
    A survey carried out at a certain hospital indicates that the probability that a patient tested positive for malaria is 0.6. What is the probability that two patients selected at random (i) one is negative while the other tested positive? (i) both patien
16. Fish tank
    A fish tank at a pet store has 8 zebra fish. In how many different ways can George choose 2 zebra fish to buy?
17. Calculation of CN
    Calculate: ?