Question

Preethi writes fifteen 1s in a row and randomly writes + and - between each pair of consecutive 1s. Find the probability that the expression that preethi wrote has value 7.

Answer 1

The probability that the expression Preeti wrote has the value 7 cannot be easily determined.

Explanation:

Given that Preeti writes

111111111111111,

then randomly writes + and - between each pair of consecutive 1's.

It is not specified that the + and - signs are written to be alternating, they are said to be just 'random'. So, there are a lot of possibilities. Things like:

1+1-1+1+1-1+1-1-1-1+1+1-1+1-1 = 1

Or

1-1-1+1+1-1-1+1+1-1+1-1+1+1-1 = -1

Or

1-1+1-1-1+1-1+1+1-1-1+1-1+1+1 = 0

And so on. There is a lot of possibilities.

So, clearly, the probability is difficult to determine, as the expression Preeti wrote could have had the value 7 in many different forms.

Because:

1+1+1+1+1+1+1-1+1-1+1-1+1-1+1 = 7

1+1+1+1-1-1-1-1-1+1-1-1-1+1+1 = 7

And many more.

Therefore, the probability that the expression Preeti wrote has the value 7 cannot be easily determined.