Lots of good advice here. I will add that there are folks out there who choose to set up their four string basses to tune BEAD, handy if you play very low tunings and don't want to deal with a fifth string. However because the strings are all thicker you'll have to file out the slots on the nut, and if you want to go back to standard tuning you'd probably need to replace the nut as EADG strings will sit loose in the nut slots you filed for BEAD strings.
Just to give some background here on string pitch - there are three things that you can do that will have a significant impact on the pitch of the string.
The first is the speaking length of the string. You are changing this every time you fret a note - shortening the length of the string makes the pitch higher. This is also why bass guitars have a longer scale length than guitars, which have longer scale length than mandolins or ukuleles.
The second is the thickness of the string. All else being equal, a thicker string will have a lower pitch than a thinner string, which is why a typical set of 4 bass strings go from about .100 to .045 inches in diameter as they go up from E to G, and furthermore why bass strings are thicker than guitar strings. However, there's a range that you can have a string tuned to a certain pitch at - for instance a low E string can be anywhere between .090 to .110 depending on the set. Which leads to the third variable that you can adjust to correct pitch...
Third is the tension or tightness of the string. You're also going to be adjusting this frequently when you tune your bass, tightening the string raises the pitch. So you can take your .105 E string and tune it down to D for a drop D tuning, and it will work pretty well (some minor intonation issues and looseness notwithstanding), but there's a point beyond which the string will be so loose that it just won't work at all. On the other end of that, you can tighten a string up a bit safely - I sometimes tune my six string guitar to open E, which raises a couple of strings up a whole note - but going up a full fourth, say from B to E, will likely cause the string core to snap.
As a beginning bass player, I'd recommend using the top four strings of the set you bought, or returning/exchanging the set for a four string one. You'll be able to do more with a single bass tuned to EADG than a BEAD bass unless you're planning to play in a doom metal band.