Thank you for visiting Three shooters shoot at the same target and each of them shoots just once The first shooter hits the target with a probability of 50. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Answer:
Let X be the number of times the target is hit. The probability P(X≥1) then equals 1 minus the probability of missing the target three times:
P(X≥1) = 1− (1−P(A)) (1−P(B)) (1−P(C))
= 1−0.4*0.3*0.2
= 0.976
To find the probability P(X≥2) of hitting the target at least twice, you can consider two cases: either two people hit the target and one does not, or all people hit the target. We find:
P(X≥2)=(0.4*0.7*0.8)+(0.6*0.3*0.8)+(0.6*0.7*0.2)+(0.6*0.7*0.8) = 0.788
Step-by-step explanation:
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Rewritten by : Jeany
Final answer:
To determine the probability that the shooters hit the target at least once and at least twice, we use the probability of them missing and then subtract from 1, followed by adjusting for the probability of only one shooter hitting the target.
Explanation:
The subject of this question is probability, specifically looking at the probability of independent events. We have three shooters with different probabilities of hitting a target once: 50%, 60%, and 70%. To calculate the probability that the shooters will hit the target at least once, we have to consider the probability that all of them miss the target and subtract it from 1 (the total probability of all possible outcomes). The probabilities of missing are 50% or 0.5 for the first shooter, 40% or 0.4 for the second shooter, and 30% or 0.3 for the third shooter. Multiplying these probabilities gives us the overall probability that all shooters miss the target.
To find the probability that the shooters hit the target at least twice, we need to calculate the probabilities of exactly one shooter hitting the target and subtract this from the probability of hitting the target at least once.
We can use a step-by-step approach for both calculations:
- Calculate the probability of each shooter missing the target by subtracting their hit probabilities from 1.
- Multiply the probabilities of all shooters missing to find the probability that none of them hit the target.
- Subtract this probability from 1 to get the probability of at least one hit.
- Calculate the probability of exactly one shooter hitting by considering all three scenarios where each shooter hits alone.
- Sum the probabilities of exactly one shooter hitting to get the total probability of exactly one hit.
- Subtract the probability of exactly one hit from the probability of at least one hit to get the probability of at least two hits.
