Blank Space Part 4

Logic Level 1

$\large 1 \, \square \, 3 \, \square \, 5$

If I were to randomly fill the squares with two (not necessarily distinct) mathematical operators out of $( +, -, \times, \div)$ , is the resultant number more likely to be positive or negative?

Note :
You are not allowed to use parenthesis.
Obey the order of operations.

Not enough information They are both equally likely Positive Negative

2 solutions

Brian Charlesworth
Jul 22, 2015

There are $4$ ways to fill each of the boxes for a total of $4^{2} = 16$ outcomes.

Using just the $+, \times$ and $\div$ operators gives us $3^{2} = 9$ outcomes, each of which is necessarily positive, implying that it is more likely for the outcome to be positive.

(Two of the outcomes using the $-$ operator are positive as well, namely $1 - 3 + 5 = 3$ and $1 - 3 \div 5 = 2 \div 5,$ giving a total of $11$ positive outcomes to only $5$ negative outcomes.)

Curiously, the average of the $16$ outcomes, all of which are distinct, is $2.$

This is incorrect. Because it doesn't specifically say that you couldn't use the same sign twice. Therefore using two subtraction signs would cause it to be negative.

Natalie Wakefield - 5 years, 10 months ago

Yes, there are outcomes that are negative such as the one you mention, but a majority of the possible outcomes are positive. Thus if the operators are chosen at random, it is more likely for the resultant number to be positive.

As an aside, if the operators did have to be distinct, then there would be $12$ possible outcomes, $4$ of which would be negative.

Brian Charlesworth - 5 years, 10 months ago

Gourab Roy
Aug 7, 2015

In easy words we can say that if we use " - " before 5 in case there is "+" or "/" between 1 and 3, it will be negative or if we use it to fill both the blanks or a "-" between 1 and 3 if there are "x" or "/" . Otherwise it is always postive

Blank Space Part 4

2 solutions

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