Your daughter is very unlikely to have TB. She has been immunised against TB at birth with the BCG. Although not completely protective againsts TB it is reasonably effective. Your domestic worker appears to be well and is HIV negative. She is unlikely to have TB. It is also unlikely that her daughter had TB. She may have had some other illness such as pneumonia.
You do not need a sputum test to diagnose TB. Usually a skin test called the Mantoux is done which is not expensive and can be done at your nearest health clinic.It does not appear necessary for your daughter to have this test done.
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