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six claims are to be randomly selected from a group of thirteen different claims, which includes two workers compensation claims, four homeowners claims and seven auto claims.

calculate the probability that the six claims selected will include one workers compensation claim, two homeowners claims and three auto claims

Respuesta :

Using the combination formula, it is found that there is a 0.2448 = 24.48% probability that the six claims selected will include one workers compensation claim, two homeowners claims and three auto claims.

  • A probability is the number of desired outcomes divided by the number of total outcomes.
  • In this problem, the order in which the claims are chosen is not important, which means that the combination formula is used to find these numbers of outcomes.

Combination formula:

[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

The desired outcomes are:

  • One workers from a set of 2.
  • Two homeowners from a set of 4.
  • Three auto-claims from a set of 7.

Thus:

[tex]D = C_{2,1}C_{4,2}C_{7,3} = \frac{2!}{1!1!} \times \frac{4!}{2!2!} \times \frac{7!}{4!3!} = 420[/tex]

For the total outcomes, six claims from a set of 13, thus:

[tex]T = C_{13,6} = \frac{13!}{6!7!} = 1716[/tex]

The probability is:

[tex]p = \frac{D}{T} = \frac{420}{1716} = 0.2448[/tex]

0.2448 = 24.48% probability that the six claims selected will include one workers compensation claim, two homeowners claims and three auto claims.

A similar problem is given at https://brainly.com/question/25112440