Ten policyholders file claims with CareFree Insurance.Three of these claims are fraudulent.Claims manager Earl Evans randomly selects three of the ten claims for thorough investigation.If x represents the number of fraudulent claims in Earl's sample, P(x=1)is _______________.
A)0.5250
B)0.4410
C)0.3000
D)0.6957
E)0.9957

Question

Quizplus · Accepted Answer

The probability of selecting exactly 1 fraudulent claim out of 3 chosen from 10, where 3 are fraudulent and 7 are legitimate, can be calculated using combinations. The probability is found by dividing the number of ways to choose 1 fraudulent and 2 legitimate claims by the total ways to choose any 3 claims from 10. This is calculated as: $\frac{{\binom{3}{1} \times \binom{7}{2}}}{{\binom{10}{3}}} = \frac{{3 \times 21}}{{120}} = 0.525$.

Ten Policyholders File Claims with CareFree Insurance