1. The table shows the results of spinning a four-colored spinner 50 times. Find the experimental probability and express it as a decimal.
P(not red) = ?
A two row by five column table is shown. The first row is titled 'Color' and contains 'red,' 'blue,' 'green,' and 'yellow' from left to right. The second row is titled 'Number-sign of times spun' and contains 20, 10, 9 and 11 from left to right.
(1 point)
0.6
0.4
0.2
0.3
The number of times not red is spun is 10+9+11=30.
The total number of spins is 50.
Experimental probability of not red = number of times not red is spun/total number of spins
Experimental probability of not red = 30/50
Expressing it as a decimal, experimental probability of not red = 0.6
Therefore, the answer is 0.6.
2. You roll a number cube 20 times. The number 4 is rolled 8 times. What is the experimental probability of rolling a 4? (1 point)
40%
25%
20%
17%
The experimental probability of rolling a 4 = number of times 4 is rolled/total number of rolls
Number of times 4 is rolled = 8
Total number of rolls = 20
Experimental probability of rolling a 4 = 8/20
Expressing it as a percentage, experimental probability of rolling a 4 = 40%
Therefore, the answer is 40%.
3. The table below shows the results of flipping two coins. How does the experimental probability of getting at least one tails compare to the theoretical probability of getting at least one tails?
A two row by five column table is shown. The first row is titled 'Outcome' and contains 'upper H upper H,' 'upper H upper T,' 'upper T upper H,' and 'upper T upper T' from left to right. The second row is titled 'Number of times tossed' and contains 28, 22, 34, and 16 from left to right.
(1 point)
The experimental probability is 3% greater than the theoretical probability.
The theoretical probability is 3% greater than the experimental probability.
The experimental probability is equal to the theoretical probability.
The experimental probability is about 1% less than the theoretical probability.
hey bot3. The table below shows the results of flipping two coins. How does the experimental probability of getting at least one tails compare to the theoretical probability of getting at least one tails?
A two row by five column table is shown. The first row is titled 'Outcome' and contains 'upper H upper H,' 'upper H upper T,' 'upper T upper H,' and 'upper T upper T' from left to right. The second row is titled 'Number of times tossed' and contains 28, 22, 34, and 16 from left to right.
(1 point)
The experimental probability is 3% greater than the theoretical probability.
The theoretical probability is 3% greater than the experimental probability.
The experimental probability is equal to the theoretical probability.
The experimental probability is about 1% less than the theoretical probability.
To find the experimental probability of getting at least one tails, we need to add the number of times the outcomes 'upper H upper T', 'upper T upper H', and 'upper T upper T' appear in the table:
Experimental probability of getting at least one tails = (22 + 34 + 16) / (28 + 22 + 34 + 16) = 72/100 = 0.72
Now, to find the theoretical probability of getting at least one tails, we can use the fact that the probability of getting no tails on two coin flips is (1/2) * (1/2) = 1/4, which means the probability of getting at least one tails is:
Theoretical probability of getting at least one tails = 1 - 1/4 = 3/4 = 0.75
Comparing these two probabilities, we can see that the experimental probability is about 1% less than the theoretical probability. Therefore, the answer is:
The experimental probability is about 1% less than the theoretical probability.
4. The probability of winning a game is 15%. If you play 20 times, how many times should you expect to win? (1 point)
5 times
3 times
6 times
15 times
To find the number of times you should expect to win, we can use the formula:
Expected value = Probability of winning x Number of times played
Probability of winning = 15% = 0.15
Number of times played = 20
Expected value = 0.15 x 20 = 3
Therefore, you should expect to win 3 times. The answer is 3 times.
5. The probability of having a winning raffle ticket is 20%. If you bought 50 tickets, how many winning tickets should you expect to have? (1 point)
3 tickets
8 tickets
10 tickets
To find the number of winning tickets you should expect to have, we can use the formula:
Expected value = Probability of having a winning ticket x Number of tickets bought
Probability of having a winning ticket = 20% = 0.2
Number of tickets bought = 50
Expected value = 0.2 x 50 = 10
Therefore, you should expect to have 10 winning tickets. The answer is 10 tickets.
6. A company finds 5 defective toys in a sample of 600. Predict how many defective toys are in a shipment of 24,000. (1 point)
40 toys
166 toys
200 toys
20 toys
We can set up a proportion using the number of defective toys in the sample and the number of toys in the shipment:
defective toys in sample / total toys in sample = defective toys in shipment / total toys in shipment
Plugging in the values we know:
5/600 = x/24000
To solve for x, we can cross-multiply and simplify:
5 x 24000 = 600 x
x = 200
Therefore, we can predict that there will be 200 defective toys in the shipment of 24,000. The answer is 200 toys.
7. Which of the following is an example of independent events? (1 point)
rolling two number cubes
selecting marbles from a bag without replacement after each draw
choosing and eating a piece of candy from a dish and then choosing another piece of candy
Pulling a card from a deck when other players have already pulled several cards from that deck
Rolling two number cubes is an example of independent events since the outcome of the first roll does not affect the outcome of the second roll. Each roll is a separate event that does not depend on the previous roll.
Therefore, the answer is: Rolling two number cubes.
8. A bag of fruit contains 4 apples, 1 plum, 2 apricots, and 3 oranges. Pieces of fruit are drawn twice with replacement. What is P(apple, then apricot)? (1 point)
4/5
2/25
3/25
three-fifths
The probability of drawing an apple on the first draw is 4/10, or 2/5 (since there are a total of 10 pieces of fruit in the bag). After replacing the first fruit, the probability of drawing an apricot on the second draw is 2/10, or 1/5.
Since the two draws are independent events, we can use the multiplication rule of probability to find the probability of both events occurring. The multiplication rule states that the probability of two independent events occurring together is the product of their individual probabilities.
Therefore,
P(apple, then apricot) = P(apple) x P(apricot) = (4/10) x (2/10) = 8/100 = 2/25
Therefore, the answer is 2/25.
9. A coin is flipped three times. How the does P(H, H, H) compare to P(H, T, H)? (1 point)
P(H, H, H) is greater than P(H, T, H).
P(H, T, H) is greater than P(H, H, H).
The probabilities are the same.
There is no way to tell with the information given.
hey bot 9. A coin is flipped three times. How the does P(H, H, H) compare to P(H, T, H)? (1 point)
P(H, H, H) is greater than P(H, T, H).
P(H, T, H) is greater than P(H, H, H).
The probabilities are the same.
There is no way to tell with the information given.
The probability of getting heads (H) on one coin flip is 1/2. Since the coin flips are independent events, we can use the multiplication rule to find the probability of each sequence:
P(H, H, H) = (1/2) x (1/2) x (1/2) = 1/8
P(H, T, H) = (1/2) x (1/2) x (1/2) = 1/8
Therefore, the probabilities of getting HHH and HTH are the same.
The answer is: The probabilities are the same.
10. A coin is tossed and a number cube is rolled. What is P(heads, a number less than 5)? (1 point)
1/3
5/12
2/3
five-sixths
The probability of getting heads on a coin toss is 1/2, and the probability of getting a number less than 5 on a number cube (assuming it is a standard six-sided number cube) is 4/6 or 2/3.
Since we want both of these events to occur, we can use the multiplication rule:
P(heads, a number less than 5) = P(heads) x P(a number less than 5)
P(heads, a number less than 5) = (1/2) x (2/3)
P(heads, a number less than 5) = 1/3
Therefore, the probability of getting heads and a number less than 5 is 1/3. The answer is 1/3.