What is the probability of contracting either glaucoma or diabetes, given P(G)=0.02, P(D)=0.025, and P(G and…

Question

What is the probability of contracting either glaucoma or diabetes, given P(G)=0.02, P(D)=0.025, and P(G and D)=0.0008?

ScanSolve AI Tutor · Accepted Answer

This problem asks for the probability of contracting either glaucoma or diabetes. This is a classic application of the formula for the probability of the union of two events.

Let $G$ be the event of contracting glaucoma.
Let $D$ be the event of contracting diabetes.

We are given the following probabilities:

The lifetime probability of contracting glaucoma: $P(G) = 0.02$
The lifetime probability of contracting diabetes: $P(D) = 0.025$
The probability of contracting both diseases: $P(G \cap D) = 0.0008$

To find the probability of contracting either glaucoma or diabetes, we use the formula for the union of two events:

P(G \cup D) = P(G) + P(D) - P(G \cap D)

Substitute the given values into the formula.
$P(G \cup D) = 0.02 + 0.025 - 0.0008$
Perform the addition.
$0.02 + 0.025 = 0.045$
Perform the subtraction.
$P(G \cup D) = 0.045 - 0.0008$ $P(G \cup D) = 0.0442$
The lifetime probability of contracting either glaucoma or diabetes is 0.0442.

Comparing this result with the given options:

a) 0.0442

b) 0.0392

c) 0.0458

d) 0.0492

Our calculated value matches option (a).

The final answer is $\boxed{\text{a) } 0.0442}$ .

What is the probability of contracting either glaucoma or diabetes, given P(G)=0.02, P(D)=0.025, and P(G and D)=0.0008?

Answer

Step-by-step solution

Substitute the given values into the formula.

Perform the addition.

Perform the subtraction.

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