There are 4 pieces of paper, numbered 10 to 13, in a hat. After another numbered piece of paper is added, the probability of picking a number between 10 and 13 inclusive is 4/5. Which of the following numbers could be the number on the new piece of paper?
A. 10
B. 11
C. 12
D. 13
E. 1
To solve this problem, we need to find the total number of pieces of paper after the new piece is added, and then determine which of the given numbers could be the number on that new piece.
Let's start by considering the initial scenario. Initially, there are 4 pieces of paper numbered 10, 11, 12, and 13 in the hat. So, the total number of pieces is 4.
Now, after the new piece is added, we need to find the total number of pieces of paper. Let's say the number on the new piece is "x." So, the total number of pieces will be 4 + 1 = 5.
According to the problem, the probability of picking a number between 10 and 13 (inclusive) after the new piece is added is 4/5. This means that out of the 5 total pieces, 4 of them should have numbers between 10 and 13.
Now, let's consider each answer choice:
A. If the new number is 10, then all the numbers from 10 to 13 (inclusive) will be present, which satisfies the given probability condition. So, option A is a possibility.
B. If the new number is 11, then all the numbers from 10 to 13 (inclusive) will be present, which satisfies the given probability condition. So, option B is a possibility.
C. If the new number is 12, then all the numbers from 10 to 13 (inclusive) will be present, which satisfies the given probability condition. So, option C is a possibility.
D. If the new number is 13, then all the numbers from 10 to 13 (inclusive) will be present, which satisfies the given probability condition. So, option D is a possibility.
E. If the new number is 1, then the numbers from 10 to 13 (inclusive) will not be present, as the range of numbers given in the options is from 1 to 13. So, option E is not a possibility.
Therefore, the numbers that could be the number on the new piece of paper are options A, B, C, and D.
In conclusion, option E is not a possible number for the new piece, and options A, B, C, and D are all possible numbers for the new piece.