A search for the standard model Higgs boson decaying to a pair of bottom quarks is presented. Higgs bosons produced in association with a \mbox{W} or \mbox{Z} boson are searched for in final states including 0, 1, or 2 charged leptons and two identified \mbox{b} jets. The search is performed at the LHC in a data sample recorded by the CMS experiment in 2017 corresponding to $41.3$ fb$^{-1}$ of \mbox{pp} collisions at $\sqrt{s}=13$ TeV. An excess of events is observed with a significance of $3.3$ standard deviations, corresponding to a measured signal strength of $1.08\pm 0.34$ times the standard model expectation. When combined with previous results using this production channel and data collected at $7$, $8$, and $13$ TeV, the observed significance increases to $4.8$ standard deviations and the measured signal strength is $1.01\pm 0.22$. A combination of all CMS searches for \mbox{H}\to\mbox{b}\bar{\mbox{b}}, including the four dominant production processes at the LHC, yields an observed (expected) significance of $5.6$ ($5.5$) standard deviations and a signal strength of $1.04\pm0.20$.

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