Answer: 1/7
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Work Shown:
A = probability 1st satellite sends weak signal
A = 3/7
B = probability 2nd satellite sends weak signal, assuming event A happens earlier
B = 2/6 = 1/3
C = probability both A and B happen at the same time
C = A*B
C = (3/7)*(1/3)
C = 3/21
C = 1/7
Note: The fraction 3/7 has both numerator and denominator decrease by 1, to get 2/6, due to the "no replacement" condition.