The Venn diagram shows the probabilities associated with three events $D$ , $E\,$ and $F$ , representing users of three social media apps. The probability of using only $D\,$ is 0.1, only $E\,$ is 0.35, and only $F\,$ is 0.2. The intersection $\cap E\,$ is $q\,$ and $\cap F\,$ is $p$ . Events $D\,$ and $F\,$ have no common outcomes. The probability of using none of the apps is $r$ .

Venn diagram of events D, E and F, with D and F disjoint and E overlapping both, showing probabilities 0.1, q, 0.35, p, 0.2 and r.

Write down the two events that are mutually exclusive.

Given that $P (E ∣ F) = 0.2$ , find the value of $p$ .

Given also that $D\,$ and $E\,$ are independent, find the values of $q\,$ and $r$ .

Venn diagram of events D, E and F, with D and F disjoint and E overlapping both, showing probabilities 0.1, q, 0.35, p, 0.2 and r.

Write down the two events that are mutually exclusive.

Given that $P (E ∣ F) = 0.2$ , find the value of $p$ .

Given also that $D\,$ and $E\,$ are independent, find the values of $q\,$ and $r$ .

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