Probability

[dtweah]

The probability that a visit to a primary care physician’s (PCP) office results in neither lab work nor referral to a specialist is 35% . Of those coming to a PCP’s office, 30% are referred to specialists and 40% require lab work. Determine the probability that a visit to a PCP’s office results in both lab work and referral to a specialist.

(A) 0.05
(B) 0.12
(C) 0.18
(D) 0.25
(E) 0.35

[DanaJ]

This is a classical type of problem involving two characteristics: the first one is lab work, the second is referral to a specialist. When you get such a problem, remember the following formula:

Total = (objects that have trait 1) + (objects that have trait 2) - (objects that have both) + (objects that have none)

In this case, you're presented with percentages. The total will be 100%:

100% = 30% + 40% - x + 35% ---- x will be 5% or 0.05.

[tryin700]

This can also be solved using Venn diagram.

If OA is A

I can provide an explainer.

[nitya34]

easy 5%


25+x+35=100-35

[cata1yst]

This is a classical type of problem involving two characteristics: the first one is lab work, the second is referral to a specialist. When you get such a problem, remember the following formula:

Total = (objects that have trait 1) + (objects that have trait 2) - (objects that have both) - (objects that have none)

In this case, you're presented with percentages. The total will be 100%:

100% = 30% + 40% - x + 35% ---- x will be 5% or 0.05.

Is there an equation for 3 objects? If so, can you explain? Thanks.

[jakesing]

I believe the formula for 3 is:

Total: (# of 1) + (# of 2) + (# of 3) - (# that have 2 of characteristics) - 2*(# that have all 3) + (# that have none).