An auto insurance company concludes that 30% of policyholders with only collision coverage will have a claim next year, 40% of policyholders with only comprehensive coverage will have a claim next year, and 50% of policyholders with both collision and comprehensive coverage will have a claim next year. Records show 60% of policyholders have collision coverage, 70% have comprehensive coverage, and all policyholders have at least one of these coverages. Calculate the percentage of policyholders expected to have an accident next year.

40% of policyholders are expected to have an accident next year

Step-by-step explanation:

Given the data in the question;

P( collision coverage ) = 60% = 0.6

P( comprehensive coverage ) = 70% = 0.7

Now, we make use of the Law of addition of probability, so

P( collision coverage and comprehensive coverage ) = P( collision coverage )  + P( comprehensive coverage ) - P( collision coverage or comprehensive coverage )

P( collision coverage and comprehensive coverage )  = 0.6 + 0.7 - 1

P( collision coverage and comprehensive coverage ) = 0.3

Now,

P( comprehensive coverage only ) = P( comprehensive coverage ) - P( collision coverage and comprehensive coverage )

P( comprehensive coverage only ) = 0.7 - 0.3

P( comprehensive coverage only ) = 0.4

And

P( collision coverage only) = P( collision coverage ) - P( collision coverage and comprehensive coverage )

P( collision coverage only) = 0.6 - 0.3 = 0.3

Next  we make use of the Law of total probability;

P( accident ) = [P( accident ║ collision coverage only) × P( collision coverage only)] + [P( accident ║ comprehensive coverage only) × P( comprehensive coverage only)] + [P( accident ║ collision coverage and comprehensive coverage only) × P( collision coverage and comprehensive coverage only)]

so we substitute in our values;

P( accident ) = [ 30% × 0.3 ] + [ 40% × 0.4 ] + [ 50% × 0.3 ]

P( accident ) = [ 0.3 × 0.3 ] + [ 0.4 × 0.4 ] + [ 0.5 × 0.3 ]

P( accident ) = 0.09 + 0.16 + 0.15

P( accident ) = 0.4 or 40%

Therefore,  40% of policyholders are expected to have an accident next year

step-by-step explanation:

let's assume

number of candles set =x

price of of x candles =p(x)

we are given

a candle maker prices one set of scented candles at $10 and sells an average of 200 sets each week

so, we get point as (200,10)

he finds that when he reduces the price by $1, he then sells 50 more candle sets each week

so, we can find slope

now, we can use point slope form of line

now, we can plug values

we can use point

and find b

now, we can plug it back

and we get

now, we can find revenue

we know that

revenue = price*quantity

so, we get

6950 is the