# Battleship Probability Question - Expected Values

Let's say you randomly select X squares from a battleship grid (let's say a 7x7 grid & no replacement), how many squares would you expect to be selected from a given column/row?

So, choose 14 squares, what's the expected value of # of squares selected from row A?

• By symmetry the expected number selected in any row is the same. Thus if $X$ squares are selected, the expected number in Row A is $X/7$. – André Nicolas Sep 17 '15 at 19:11
• $2$. Hint: expected number of squares selected from a square is $14/49$. – zhoraster Sep 17 '15 at 19:22

This sort of question can be answered using the linearity of expectation. Each square has a probability of $p=X/49$ of being selected. Thus the expected number of squares selected out of $1$ square is $p\cdot1+(1-p)\cdot0=p$, so by linearity of expectation the expected number of squares selected out of $7$ squares is $7X/49=X/7$.
• @user271746: Alternatively: The expected number of squares selected on the entire grid is $X$. By linearity of expectation, this is $7$ times the expected number of squares per row, which is thus $X/7$. – joriki Sep 17 '15 at 19:20