Conditional probability practice

Could anyone please explain why P(A/B) > 0.5?

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If two things are positively correlated than one happens the other is also likely to happen.

I screen 100 stocks on two valuation sceens ranking either “high” or “low”
Price to Book (PB) 50 stocks “high” 50 stocks “low”
Price to Earnings (PE) 50 stocks “high” 50 stocks “low”

Draw a probability tree diagram with 2 screens
Say we do the PB screen first and we split 50/50 high/low
Now think of the 50 high PB stocks,
If the PE was indepenant we would again split 50/50 high low

But they are not independant so if a stock is “high” PB it is MORE likely to be high PE.

Is the Prob(high PE given higher PB) > Prob(high PE IF they independant events)
Prob(high PE given higher PB) > 0.5 i.e 0.6


Thank you so much