Of a group of patients having injuries, 28% visit both a physical therapist and a chiropractor and 8% visit neither. Say that the probability of visiting a physical therapist exceeds the probability of visiting a chiropractor by 16%. What is the probability of a randomly selected person from this group visiting a physical therapist?
Please, help

Question

Of a group of patients having injuries, 28% visit both a physical therapist and a chiropractor and 8% visit neither. Say that the probability of visiting a physical therapist exceeds the probability of visiting a chiropractor by 16%. What is the probability of a randomly selected person from this group visiting a physical therapist?
Please, help

loser66 · Answer

I can use Venn diagram to solve this problem and get the correct answer. However, I don't know how to put it in logic of P(T), P(C) ... and so on
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So that the probability visiting a physical therapist is 0.68. That's correct answer. But how to approach the problem algebraically?

fibonaccichick666 · Answer

Of a group of patients having injuries, 28% [P(P+C)]visit both a physical therapist and a chiropractor and 8%[P(N) ]visit neither. Say that the probability of visiting a physical therapist exceeds the probability of visiting a chiropractor by 16%.[P(C+16%)] What is the probability of a randomly selected person from this group visiting a physical therapist?
Please, help
I would probably write in those translations first, personally, I'd use the venn rather than algebraic exp in this

loser66 · Answer

Can we write  $P(P\cap C) = 0.28$

fibonaccichick666 · Answer

but anyways, we know it must add to 100%, so now we develop an exquation
$$P(P+C)+P(N)+P(C)+P(C+.16)=1$$

fibonaccichick666 · Answer

yea, you could, that would be much better actually

loser66 · Answer

neither of them is$P(P\cap C)' = 0.08$ right?

fibonaccichick666 · Answer

remind me what the ' stands for again, it's been a while.   Is that complement?

loser66 · Answer

yeah, I think so!!

fibonaccichick666 · Answer

ok, so the complement to intersect sounds alright here

fibonaccichick666 · Answer

@kirbykirby , please jump in if you wish

loser66 · Answer

Let me try on this, will post and need check. The semester starts on next Monday, I just read the book before hand, hihihi

fibonaccichick666 · Answer

ah, yea, my classes haven't started and already I have hw too... it's killer, the book sucks

loser66 · Answer

Ok, I let P(T) instead of P (P) for physical Therapist
now, I have $$\P(T\cap C) =0.28\P(T) = P(C) + 0.16\P (T) + P(C) +P(T\cap C) + P(T\cup C)'= 1$$
and solve for P(T) to get 0.68

loser66 · Answer

what is your class?

loser66 · Answer

I have a killer for this semester, too. It's called "Modern Algebra" hihihi

fibonaccichick666 · Answer

I have Analysis of single variable Calculus :/ and that looks acceptable