Final answer:
The probability that the same person will win both drawings is 1/100.
Step-by-step explanation:
The probability that the same person will win both drawings can be calculated by multiplying the individual probabilities of winning each drawing together.
Since there are 10 people participating in the drawings, the probability of one person winning the trip to Hawaii is 1/10 and the probability of winning the new car is also 1/10. To find the probability of winning both, multiply the two probabilities together:
P(winning both drawings) = P(winning trip to Hawaii) x P(winning new car) = 1/10 x 1/10 = 1/100
Therefore, the probability that the same person will win both drawings is 1/100.