NAIROBI, Kenya—As young pitchmen shout to potential passengers over blaring music, a graffiti-covered private minibus fills up more quickly than the other dozen in the scrum. It has free Wi-Fi.

The specially outfitted matatu, as the minibuses are known in Swahili, is part of an experiment by Safaricom Ltd. to connect Africa's unconnected, offering a glimpse of what it takes to bring some of the world's most price-sensitive users online.

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