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"Channel One" is an educational television network for which participating secondary schools are equipped with TV sets in every classroom. It has been found that 70% of secondary schools subscribe to Channel One, where of these subscribers 5% never use Channel One while 25% claim to use it more than 5 times per week.

Find the probability that a randomly selected secondary school subscribes to Channel One and uses it more than 5 times per week.

I have reasoned that

$P(A) = 0.7$ from the number of secondary schools subscribed to channel one

$P(B) = 0.25$ claim to use it more than 5 times per week.

\begin{align} P(A \cup B) &= P(A) + P(B) - P(A \cap B)\\ &= 0.7 + 0.25 - (0.70)(0.25)\\ &= 0.775 \end{align}

What is the correct answer and solution?

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Your question is that for a randomly selected secondary school, that this school subscribes and uses it more than 5 times per week.

So we want $$P(A \cap B)= 0.70 \cdot 0.25$$ You computed the wrong probability, the 25% is for the schools that are subscribed, so give that we are part of the 70%, 25% of those schools claim to use the subscription more than 5 times per week.

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  • $\begingroup$ Thank you and all the best! $\endgroup$
    – Alexis
    Jan 31, 2017 at 23:25

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