Game wardens use experiments to help determine the number of raccoons in a forest. Suppose 60 raccoons are caught, tagged, and released back into the forest. Two weeks later 40 raccoons are caught, of which 4 are found to have tags. Estimate the number of raccoons in the forest.
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2,400 raccoons
56 raccoons
600 raccoons
96 raccoons
2. A bag contains 4 yellow marbles and 6 green marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn. What is the probability that the first marble is green and the second one is yellow?
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4/15
1/15
3/2
1/6
3. A bag contains 2 red marbles and 4 green marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then a second marble is drawn. What is the probability that the first marble is green and the second one is red?
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2
2/15
4/15
1/4
4. A coin is tossed and a number cube is rolled. What is the probability that the coin shows heads and the number cube shows an odd number?
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1/4
1/12
1
1/6
5. A number cube is rolled 300 times and the results recorded: 48 ones, 53 twos, 42 threes, 51 fours, 50 fives, and 56 sixes. What is the experimental probability of NOT rolling a five?
0.07
0.83
0.17
0.93
6. Which events are independent?
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You choose 2 different ice cream flavors.
You study English 20 min nightly, then you get an A on the next test.
You draw a card from a deck, replace it and draw a second.
You draw a card and don't replace it. Then you draw another.
You choose 2 different ice cream flavors.
You draw a card from a deck, replace it and draw a second.
1. To estimate the number of raccoons in the forest, we can set up a proportion using the results of the tagged raccoons.
Let x be the estimated number of raccoons in the forest.
Based on the information given, the ratio of tagged raccoons to the total number of raccoons in the second catch is equal to the ratio of tagged raccoons to the total number of raccoons in the forest.
(4 tagged raccoons) / (40 total raccoons) = (60 tagged raccoons) / (x total raccoons)
Cross-multiplying, we get 4x = 2400.
Dividing both sides by 4, we find that x = 600.
Therefore, the estimated number of raccoons in the forest is 600.
Answer: 600 raccoons
2. The probability that the first marble drawn is green and the second marble drawn is yellow can be calculated as follows:
The probability of drawing a green marble on the first draw is 6/10 since there are 6 green marbles out of a total of 10 marbles.
After removing a green marble, there are now 9 marbles remaining, with 4 of them being yellow.
The probability of drawing a yellow marble on the second draw is 4/9.
To find the probability of both events happening, we multiply the probabilities together:
(6/10) * (4/9) = 24/90 = 4/15
Therefore, the probability that the first marble is green and the second marble is yellow is 4/15.
Answer: 4/15
3. The probability that the first marble drawn is green and the second marble drawn is red can be calculated as follows:
The probability of drawing a green marble on the first draw is 4/6 since there are 4 green marbles out of a total of 6 marbles.
After removing a green marble, there are now 5 marbles remaining, with 2 of them being red.
The probability of drawing a red marble on the second draw is 2/5.
To find the probability of both events happening, we multiply the probabilities together:
(4/6) * (2/5) = 8/30 = 4/15
Therefore, the probability that the first marble is green and the second marble is red is 4/15.
Answer: 4/15
4. The probability that the coin shows heads and the number cube shows an odd number can be calculated as follows:
The probability of the coin showing heads is 1/2 since there are two possible outcomes (heads or tails) and it is a fair coin.
The probability of the number cube showing an odd number is 3/6 since there are three odd numbers (1, 3, and 5) out of a total of six possible outcomes.
To find the probability of both events happening, we multiply the probabilities together:
(1/2) * (3/6) = 3/12 = 1/4
Therefore, the probability that the coin shows heads and the number cube shows an odd number is 1/4.
Answer: 1/4
5. The experimental probability of NOT rolling a five can be calculated by subtracting the number of times a five was rolled from the total number of rolls, and then dividing by the total number of rolls.
The total number of rolls was 300.
The number of times a five was rolled was 50.
The number of times NOT rolling a five occurred is 300 - 50 = 250.
Therefore, the experimental probability of NOT rolling a five is 250/300, which simplifies to 5/6 or approximately 0.83.
Answer: 0.83
6. The events that are independent are:
- You choose 2 different ice cream flavors.
- You draw a card from a deck, replace it, and draw a second.
Independent events are those where the outcome of one event does not affect the outcome of the other event. In both of these scenarios, the first event does not impact the probability of the second event.
The other two events mentioned are not independent:
- Studying English nightly and getting an A on the next test: Studying can increase the likelihood of getting an A.
- Drawing a card and not replacing it, then drawing another: The probability of drawing the second card depends on which card was drawn first since the deck is not being replaced.
Answer: You choose 2 different ice cream flavors. and You draw a card from a deck, replace it, and draw a second. are independent events.