tmua.me Extreme Set B Paper 2 · Question 6

Three coins $A$ , $B$ and $C$ are tossed independently. Their probabilities of landing heads are $p$ , $q$ and $r$ , respectively, where

0<p<1,\qquad 0<q<1,\qquad 0<r<1.

Let $S$ be the event that $A$ and $B$ show the same result, and let $T$ be the event that $B$ and $C$ show the same result.

Consider the propositions

Is P necessary and/or sufficient for Q?

AP is neither necessary nor sufficient for Q

BP is necessary but not sufficient for Q

CP is sufficient but not necessary for Q

DP is necessary and sufficient for Q

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