# Probability of Missed Bullseye 3+ Times in 4 Shots

• MHB
• SteffiB
In summary, the probability of missing the bullseye 3+ times in 4 shots is 1/16 or 0.0625. To calculate the probability, you can use the binomial probability formula. It is possible to miss the bullseye 3+ times in 4 shots, and as the number of shots increases, the probability also increases. The main factor that can affect the probability is the accuracy of the shooter, but distance, wind, and distractions may also play a role.
SteffiB
1.Mary has two friends, Ann and Sarah. Mary will visit Ann this evening if the 19A bus arrives before 6PM. Otherwise, She will visit Sarah. The probability of the 19A bus arriving before 6pm is 40%. If she visits Ann, the probability that Ann will be at home is 10% and if she visits Sarah, the probability that Sarah will be home is 20%. Find the probability that the friend Mary visits will be home

2.A darts player finds that on average he hits the bullseye 4 times out of 5. Calculate the probability that in a random sample of 4 shots, he will miss the bullseye at least 3 times

SteffiB said:
1.Mary has two friends, Ann and Sarah. Mary will visit Ann this evening if the 19A bus arrives before 6PM. Otherwise, She will visit Sarah. The probability of the 19A bus arriving before 6pm is 40%. If she visits Ann, the probability that Ann will be at home is 10% and if she visits Sarah, the probability that Sarah will be home is 20%. Find the probability that the friend Mary visits will be home
Imagine this happenng 1000 times. 40% of the time, 400 times, she visits Ann. 10% of those, 40 times, Ann is home. 100- 40= 60% of the time, 600 times, she visits Sarah. 20% of those, 120 times, Sarah is home. So of the 1000 times, the person she visits is home 40+ 120= 160 times. The probably the person she visits will be home is 160/1000= 16%.

2.A darts player finds that on average he hits the bullseye 4 times out of 5. Calculate the probability that in a random sample of 4 shots, he will miss the bullseye at least 3 times
Since, on average, he hits the bullseye "4 times out of 5" the probability he will hit the bullseye on anyone shot is 4/5 and the probability he misses is 1- 4/5= 1/5. "At least 3 times" in 4 shots is either "all 4 shots" or "3 out 4 shots". The probability of missing "all 4 shots" is (1/5)(1/5)(1/5)(1/5)= 1/5^4= 1/625. One way of missing "3 out of 4 shots" is to miss the first three shots and hit the last one. The probability of that is (1/5)(1/5)(1/5)(4/5)= 4/5^4= 4/635. But you could also miss the first two, hit the third and then miss the fourth. That is also (1/5)(1/5)(4/5)(1/5) which is also 4/625. There are also "Hit, Miss, Hit, Hit" and "Miss, Hit, Hit, Hit". There are four such orders and tne probability of each is 4/625. That means that the probability of "three misses and one hit", in any order, is 4(4/625)= 16/625.

The probability of "at least three misses" is the sum, 1/625+ 16/625= 17/625.

## What is the probability of missing the bullseye 3+ times in 4 shots?

The probability of missing the bullseye 3+ times in 4 shots depends on the accuracy of the shooter. If the shooter has a high accuracy, the probability of missing 3+ times is low. However, if the shooter has a lower accuracy, the probability may be higher.

## How can the probability of missing the bullseye 3+ times in 4 shots be calculated?

The probability of missing the bullseye 3+ times in 4 shots can be calculated using the binomial distribution formula. This formula takes into account the number of trials (4 shots), the probability of success (hitting the bullseye), and the number of successes (missing the bullseye 3+ times).

## What factors can affect the probability of missing the bullseye 3+ times in 4 shots?

The accuracy of the shooter, the distance from the target, and external factors such as wind or distractions can all affect the probability of missing the bullseye 3+ times in 4 shots. The probability may also vary depending on the type of weapon or equipment being used.

## Is it possible to decrease the probability of missing the bullseye 3+ times in 4 shots?

Yes, the probability can be decreased by improving the shooter's accuracy through practice and training. Additionally, eliminating external factors such as wind or distractions can also decrease the probability of missing the bullseye 3+ times in 4 shots.

## What other statistical methods can be used to analyze the probability of missing the bullseye 3+ times in 4 shots?

Other statistical methods such as hypothesis testing or confidence intervals can also be used to analyze the probability of missing the bullseye 3+ times in 4 shots. These methods can provide more information about the accuracy of the shooter and the likelihood of missing the bullseye multiple times in a given number of shots.

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