A can hit a target 4 times in 5 shots, B 3 times in 4 shots; C twice in 3 shots. They fire atarget. What is the probability that at least two shots hit?
Question
A can hit a target 4 times in 5 shots, B 3 times in 4 shots; C twice in 3 shots. They fire atarget. What is the probability that at least two shots hit?
Solution
To solve this problem, we need to consider all the possible ways at least two shots can hit the target. This includes the scenarios where exactly two shots hit, exactly three shots hit, and all three shots hit.
-
Exactly two shots hit:
- A and B hit, C misses. The probability is (4/5) * (3/4) * (1/3) = 0.2
- A and C hit, B misses. The probability is (4/5) * (1/4) * (2/3) = 0.1333
- B and C hit, A misses. The probability is (1/5) * (3/4) * (2/3) = 0.1 The total probability for exactly two shots hit is 0.2 + 0.1333 + 0.1 = 0.4333
-
Exactly three shots hit:
- All three hit. The probability is (4/5) * (3/4) * (2/3) = 0.4
-
All three shots hit:
- The probability is the same as the scenario where exactly three shots hit, which is 0.4
So, the total probability that at least two shots hit is the sum of the probabilities for the three scenarios, which is 0.4333 + 0.4 = 0.8333 or approximately 83.33%.
Similar Questions
Three Persons A, B And C Shoot To Hit A Target. If In Trials, A Hits The Target 4 Times In 5 Shots, B Hits 3 Times In 4 Shots And C Hits 2 Times In 3 Trials. Find The Probability That Exactly Two Persons Hit The Target
e correct answerRAMU can hit a target 3 times in 6 shots, SIVA can hit the target 2 times in 6 shots and SHYAM can hit 4 times in 4 shots. What is the probability that at least 2 shots hit the targetOptions5/21/32/35/6
The probability of a shooter hitting the bullseye is 3/4. What is the probability of hitting the bullseye at least 3 times out of 5? Ops: A. 359/412 B. 322/421 C. 443/512 D. 459/512
In a video game, the player conducts shooting training. Each shot has a probability of 0.7 to hit and a probability of 0.3 to miss. The player shoots three times in a row. Please calculate the probability of the following situations:Exactly one hit（Round to three decimal places）？
Barbara played 25 rounds of Gorri and kept a tally of her success at hitting the target. Hits 0 1 2 3 4 5 6 7 8 9 10 Frequency 2 1 6 5 1 2 0 3 4 1 0 What is the probability that Barbara will hit the target at least 7 times in the next two rounds? (4 marks)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.