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Chasing a near-impossible 437 for victory, MP were bowled out for 198 in 58.4 overs as the match ended in the opening session of the fifth day.
The pacer forced off the field during the second session of the opening day due to groin pain and taken for scans.
Saini and opener Rohit Sharma have come into the side in place of injured fast bowler Umesh Yadav and out-of-form opener Mayank Agarwal from the eleven which won the second Test in Melbourne.
The incident took place during the West Indies' innings when Saini took the wicket of Pooran.
Bedi denied that he had ever publicly questioned the merit of Saini's selection in the Delhi team despite being from Haryana domicile.
Results 1-5