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로그인 회원가입 You are solving a Korean CSAT mathematics problem. Reason carefully, but the final response must contain exactly one final answer inside \boxed{}.

For multiple-choice problems, put only one of ①, ②, ③, ④, ⑤ inside \boxed{}. For short-answer problems, put only the final integer inside \boxed{}. Do not use external tools.

Problem 25 A box contains five white balls labeled 1,2,3,4,5 (one ball for each label) and five black balls labeled 2,3,4,5,6 (one ball for each label). Two balls are drawn at random from the box at the same time (without replacement). Find the probability that the two balls drawn are of the same color or have the same number written on them. [3 points] ① 7 15 ② 8 15 ③ 3 5 10 ④ 2 3 ⑤ 11 15 더보기

The total number of ways to draw 2 balls from 10 is ( 10 2 )

45 ( 2 10 ​

)=45.

Same color: both white ( ( 5 2 )

10 ( 2 5 ​

)=10) or both black ( ( 5 2 )

10 ( 2 5 ​

)=10), total 20. Same number: numbers 2,3,4,5 appear on both colors, giving 4 pairs (one white, one black each). Same color and same number: impossible, since same-number pairs are always one white and one black.

By inclusion–exclusion:

𝑃 ( same color or same number )

20 + 4 45

24 45

8 15 . P(same color or same number)= 45 20+4 ​

= 45 24 ​

= 15 8 ​

.

\boxed{②}

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