(Johnsonbough) A coin with probability [math]p[/math] for heads is tossed [math]n[/math] times. Let [math]E[/math] be the event “a head is obtained on the first toss' and [math]F_k[/math] the event `exactly [math]k[/math] heads are obtained.” For which pairs [math](n,k)[/math] are [math]E[/math] and [math]F_k[/math] independent?

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