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4 problems match “classical probability”. Clear

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1. Blue balls with twice the red probability ●○○○○ 10 ptsA bag contains 6 red balls and some blue balls. The probability of drawing a blue ball from the bag is twice the probability of drawing a red ball. Find the number of blue balls in the bag.
2. Birthday not in December ●○○○○ 10 ptsIgnoring leap years, what is the probability that a randomly chosen person's birthday is not in December? Give your answer as a decimal rounded to three decimal places.
3. First, fifteenth or last ball red ●●○○○ 20 ptsA box contains 100 balls, of which 40 are red. The balls are drawn from the box one at a time at random, without replacement. Determine: 1. the probability that the first ball drawn is red, 2. the probability that the fifteenth ball drawn is red, 3. the probability that the last ball drawn is red. Give each answer as a decimal.
4. False propositions about events ●●○○○ 20 ptsConsider the following five propositions. ① Toss a coin twice. Let event $A$ be "both tosses land heads" and event $B$ be "both tosses land tails"; then $A$ and $B$ are complementary events. ② In proposition ①, $A$ and $B$ are mutually exclusive events. ③ Among 10 products, 3 are defective. Three products are selected at random. Let event $A$ be "at most 2 of the selected products are defective" and event $B$ be "at least 2 of the selected products are defective"; then $A$ and $B$ are mutually exclusive events. ④ If events $A$ and $B$ satisfy $P(A)+P(B)=1$, then $A$ and $B$ are complementary events. ⑤ If $A$ and $B$ are mutually exclusive events, then $\overline{A}\cup\overline{B}$ is a certain event. Identify all the false propositions among these five and give their numbers, in increasing order.