An archer misses the target on her first shot and hits the target on the next 3 shots. What is the least number of consecutive shots that she must now make in order to have hit the target on at least 9/10 of all her shots?
( please show work on how to derive the answer!! Thx!)
A) 5
B) 6
C) 7
D) 9
E) 10
To find the least number of consecutive shots she must make to hit the target on at least 9/10 of all her shots, we need to determine the total number of shots she must make and then find the least number of consecutive hits she needs.
Let's assume she needs to make N consecutive shots.
- On her first shot, she misses the target.
- On her next 3 shots, she hits the target successfully.
So far, she has made 3 hits out of a total of 4 shots.
Now, we need to consider the maximum number of consecutive misses she can have to achieve hitting the target on at least 9/10 of all her shots.
If she misses on the next shot (the 5th shot), the total number of shots she would have made is 5. Out of these 5 shots, she has made 3 hits (the first 3 shots) and 1 miss (the 4th shot). Therefore, she will be left with 1 miss to achieve at least 9/10 hits.
To determine the least number of consecutive shots she must now make, we need to find how many more shots she needs to reach a total of 10 shots. Since she already made 5 shots, she needs 5 more shots.
So, the least number of consecutive shots she must now make is 5.
Therefore, the answer is A) 5.