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Cricket Australia said Monday that Finch injured a knee while batting in the fifth Twenty20 in St. Lucia last Friday and that his fitness for the ODI series will be assessed on a day-to-day basis.
Carey has previously captained the Adelaide Strikers, the South Australian Redbacks and Australia A.
The second ODI is set for Thursday and the final match on Saturday, all at Kensington Oval. West Indies won the T20 series 4-1, including the first three matches.