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A property and casualty insurance company categorizes its policyholders into three groups: low risk, medium risk, or high risk. 25% of the policyholders are low risk and 30% are high risk. The high risk policyholders are three times as likely as medium risk policyholders to file an insurance claim and the medium risk policyholders are twice as likely as the low risk policyholders to file an insurance claim. Determine the proportion of the insurance claims filed by medium risk policyholders.

Sagot :

Answer:

The correct approach is "0.39".

Explanation:

The given values are:

Low risk percentage,

= 25%

i.e.,

= 0.25

High risk percentage,

= 30%

i.e.,

= 0.30

Now,

The medium risk percentage will be:

= [tex]1-(low+high)[/tex]

= [tex]1-(0.25+0.30)[/tex]

= [tex]1-0.55[/tex]

= [tex]0.45[/tex]

Should let probability of either an assertion by a low-risk policyholder be p,

Percentage of medium risk policyholder will be,

= 2p

Percentage of high risk policyholder will be,

= 3×2p

= 6p

By applying Bayes' theorem, we get

⇒ [tex]P(A | B) = \frac{P(A \$ B)}{P(B)}[/tex]

⇒               [tex]=\frac{(0.25p + 0.45\times 2p)}{(0.25p + 0.45\times 2p + 0.30\times 6p)}[/tex]

⇒               [tex]=\frac{1.15}{2.95}[/tex]

⇒               [tex]=0.39[/tex]

Answer:

the approach is "0.39"

Explanation:

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