#### Answer

$3$

#### Work Step by Step

The number of surveyed students who do not plan to take biology, chemistry, or physics during their first year is represented in the Venn diagram by the region outside of the three circles.
The total of the students represented by the three sets is equal to the sum of all of the cardinalities inside of the three circles:
$=22+4+2+8+9+7+15
\\=67$
Since there were $70$ students surveyed, the remaining $3$ students do not plan to take any of the three subjects mentioned above during their first year.
Thus, the answer is $3$.