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
c) at least twice

Correct result:

a =  0.092
b =  0.994
c =  0.902

Solution:

p1=0.7 p2=0.8 p3=0.9  n1=1p1=10.7=310=0.3 n2=1p2=10.8=15=0.2 n3=1p3=10.9=110=0.1  a=p1 n2 n3+n1 p2 n3+n1 n2 p3=0.7 0.2 0.1+0.3 0.8 0.1+0.3 0.2 0.9=23250=0.092p_{1}=0.7 \ \\ p_{2}=0.8 \ \\ p_{3}=0.9 \ \\ \ \\ n_{1}=1-p_{1}=1-0.7=\dfrac{ 3 }{ 10 }=0.3 \ \\ n_{2}=1-p_{2}=1-0.8=\dfrac{ 1 }{ 5 }=0.2 \ \\ n_{3}=1-p_{3}=1-0.9=\dfrac{ 1 }{ 10 }=0.1 \ \\ \ \\ a=p_{1} \cdot \ n_{2} \cdot \ n_{3}+n_{1} \cdot \ p_{2} \cdot \ n_{3}+n_{1} \cdot \ n_{2} \cdot \ p_{3}=0.7 \cdot \ 0.2 \cdot \ 0.1+0.3 \cdot \ 0.8 \cdot \ 0.1+0.3 \cdot \ 0.2 \cdot \ 0.9=\dfrac{ 23 }{ 250 }=0.092
b1=p1 p2 n3+n1 p2 p3+p1 n2 p3=0.7 0.8 0.1+0.3 0.8 0.9+0.7 0.2 0.9=199500=0.398 b2=p1 p2 p3=0.7 0.8 0.9=63125=0.504  b=a+b1+b2=0.092+0.398+0.504=497500=0.994b_{1}=p_{1} \cdot \ p_{2} \cdot \ n_{3}+n_{1} \cdot \ p_{2} \cdot \ p_{3}+p_{1} \cdot \ n_{2} \cdot \ p_{3}=0.7 \cdot \ 0.8 \cdot \ 0.1+0.3 \cdot \ 0.8 \cdot \ 0.9+0.7 \cdot \ 0.2 \cdot \ 0.9=\dfrac{ 199 }{ 500 }=0.398 \ \\ b_{2}=p_{1} \cdot \ p_{2} \cdot \ p_{3}=0.7 \cdot \ 0.8 \cdot \ 0.9=\dfrac{ 63 }{ 125 }=0.504 \ \\ \ \\ b=a+b_{1}+b_{2}=0.092+0.398+0.504=\dfrac{ 497 }{ 500 }=0.994
c=b1+b2=0.398+0.504=451500=0.902c=b_{1}+b_{2}=0.398+0.504=\dfrac{ 451 }{ 500 }=0.902



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Please write to us with your comment on the math problem or ask something. Thank you for helping each other - students, teachers, parents, and problem authors.

Showing 0 comments:
avatar




Tips to related online calculators
Would you like to compute count of combinations?

You need to know the following knowledge to solve this word math problem:

Next similar math problems:

  • Candies
    bonbons_2 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? ?
  • Cards
    cards_2 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
  • Shooters
    soldiers 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.
  • Lottery
    lottery Fernando has two lottery tickets each from other lottery. In the first is 973 000 lottery tickets from them wins 687 000, the second has 1425 000 lottery tickets from them wins 1425 000 tickets. What is the probability that at least one Fernando's ticket
  • Six questions test
    binomial_1 There are six questions in the test. There are 3 answers to each - only one is correct. In order for a student to take the exam, at least four questions must be answered correctly. Alan didn't learn at all, so he circled the answers only by guessing. What
  • Birth
    probability Let's assume that the probability of the birth of a boy and a girl in the family is the same. What is the probability that in a family with five children, the youngest and oldest child is a boy?
  • Balls
    spheres From the urn in which are 7 white balls and 17 red, gradually drag 3-times without replacement. What is the probability that pulls balls are in order: red red red?
  • Hearts
    hearts_cards 5 cards are chosen from a standard deck of 52 playing cards (13 hearts) with replacement. What is the probability of choosing 5 hearts in a row?
  • Normal distribution GPA
    normal_d_3 The average GPA is 2.78 with a standard deviation of 4.5. What are students in the bottom the 20% having what GPA?
  • Test
    test_4 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
  • Today in school
    skola There are 9 girls and 11 boys in the class today. What is the probability that Suzan will go to the board today?
  • Cards
    cards_4 The player gets 8 cards of 32. What is the probability that it gets a) all 4 aces b) at least 1 ace
  • One green
    gulicky 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?
  • Class - boys and girls
    kresba In the class are 60% boys and 40% girls. Long hair has 10% boys and 80% girls. a) What is the probability that a randomly chosen person has long hair? b) The selected person has long hair. What is the probability that it is a girl?
  • Records
    binomial_1 Records indicate 90% error-free. If 8 records are randomly selected, what is the probability that at least 2 records have no errors?
  • Medicine
    lieky We test medicine on 6 patients. For all drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work?
  • Win in raffle
    tombola_1 The raffle tickets were sold 200, 5 of which were winning. What is the probability that Peter, who bought one ticket will win?