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:

$$\begin{gathered} p_1=0.7 \\ {p}_2=0.8 \\ {p}_3=0.9 \\ {n}_1=1-p_1=1-0.7={\displaystyle \frac{3}{10}}=0.3 \\ {n}_2=1-p_2=1-0.8={\displaystyle \frac{1}{5}}=0.2 \\ {n}_3=1-p_3=1-0.9={\displaystyle \frac{1}{10}}=0.1 \\ a=p_1\cdot n_2\cdot n_3+n_1\cdot p_2\cdot n_3+n_1\cdot n_2\cdot p_3=0.7\cdot 0.2\cdot 0.1+0.3\cdot 0.8\cdot 0.1+0.3\cdot 0.2\cdot 0.9={\displaystyle \frac{23}{250}}=0.092 \end{gathered}$$

$$\begin{gathered} b_1=p_1\cdot p_2\cdot n_3+n_1\cdot p_2\cdot p_3+p_1\cdot n_2\cdot p_3=0.7\cdot 0.8\cdot 0.1+0.3\cdot 0.8\cdot 0.9+0.7\cdot 0.2\cdot 0.9={\displaystyle \frac{199}{500}}=0.398 \\ {b}_2=p_1\cdot p_2\cdot p_3=0.7\cdot 0.8\cdot 0.9={\displaystyle \frac{63}{125}}=0.504 \\ b=a+b_1+b_2=0.092+0.398+0.504={\displaystyle \frac{497}{500}}=0.994 \end{gathered}$$

$c=b_1+b_2=0.398+0.504={\displaystyle \frac{451}{500}}=0.902$

Try another example

Showing 0 comments:

Next similar math problems:

• Probability of intersection
  Three students have a probability of 0.7,0.5 and 0.4 to graduated from university respectively. What is the probability that at least one of them will be graduated?
• 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.
• Shooter
  The probability that a good shooter hits the center of the target circle I is 0.1. The probability that the target hit intercircle is II 0.58. What is the probability that it hits the target circle I or II?
• 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 resolve
• Double probability
  The probability of success of the planned action is 60%. What is the probability that success will be achieved at least once if this action is repeated twice?
• Lion or virgin
  We toss coin, every throw fits lion or a virgin with equal probability 1/2. Determine how much at least we have to make throws that with probability 0.9 lion fell at least once.
• The shooter
  The shooter shoots at the target, assuming that the individual shots are independent of each other and the probability of hitting each of them is 0.2. The shooter fires until he hits the target for the first time, then stop firing. (a) What is the most li
• 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
• The accompanying
  The accompanying table gives the probability distribution of the number of courses randomly selected student has registered Number of courses 1 2 3 4 5 6 7 Probability 0.02 0.03 0.1 0.3 0.4 - 0.01 respectively. a) Find the probability of a student registe
• Alarm systems
  What is the probability that at least one alarm system will signal the theft of a motor vehicle when the efficiency of the first system is 90% and of the independent second system 80%?
• The big clock
  The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00
• Centroid - two bodies
  A body is composed of a 0.8 m long bar and a sphere with a radius of 0.1m attached so that its center lies on the longitudinal axis of the bar. Both bodies are of the same uniform material. The sphere is twice as heavy as the bar. Find the center of gravi
• Wimbledon finals
  Serena Williams made a successful first serve 67% 0f the time in a Wimbledon finals match against her sister Venus, If she continues to serve at the same rate the next time they play and serves 6 times in the first game, determine the probability that: 1.
• Probability - tickets
  What is the probability when you have 25 tickets in 5000 that you not wins the first (one) prize?
• Phone numbers
  How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
• Dices throws
  What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
• Two cars
  From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what