If we assume that the stars of one galaxy (A) are distributed uniformly at random within a circular area in the galactic plane, and the other galaxy (B) is moving perpendicular to the plane of A and passes entirely through the circle containing stars, and assume that stars in galaxy B are point-like, then:

Expected Number of collisions = Number of stars in galaxy B * cross sectional area of star in A / average area of galactic circle per star in A.

https://www.wolframalpha.com/input?i=%28number+of+stars+in+m...

says it comes to 0.5 - 1.0 (the uncertainty comes from number of stars in the milky way)

My assumptions are bad enough that it could be off by a factor of 100 one way or the other (there should be a few factors of 4/pi, it looks like Andromeda is about twice the size of the Milky Way, the average star is smaller than the sun, no stars are point like, gravity probably does something, stars are much more densely packed towards the galactic center, I'm calculating the result one galaxy passing through another, not a merger in which they might partially intersect more than once).