bot answer this question Eva wants to know the probability of tossing “heads” at least three times out of five. She used the random number table to simulate flipping a coin. She assigned odd digits to represent “heads” and even digits, including zero, to represent “tails.”
32766 53855 34591 27732
47406 31022 25144 72662
03087 35521 26658 81704
56212 72345 44019 65311
Use the table to find P(“heads” at least 3 out of 5 times).
A. three-eighths
B. seven-eighths
C. five-sixteenths
D. thirteen-sixteenths
To find the probability of getting "heads" at least 3 times out of 5, we need to add the probabilities of getting 3, 4, or 5 heads.
- 32766: 3 "heads" out of 5
- 53855: 4 "heads" out of 5
- 34591: 3 "heads" out of 5
- 27732: 2 "heads" out of 5 (not useful)
- 47406: 2 "heads" out of 5 (not useful)
- 31022: 1 "head" out of 5 (not useful)
- 25144: 2 "heads" out of 5 (not useful)
- 72662: 3 "heads" out of 5
- 03087: 2 "heads" out of 5 (not useful)
- 35521: 3 "heads" out of 5
- 26658: 2 "heads" out of 5 (not useful)
- 81704: 0 "heads" out of 5 (not useful)
- 56212: 1 "head" out of 5 (not useful)
- 72345: 2 "heads" out of 5 (not useful)
- 44019: 1 "head" out of 5 (not useful)
- 65311: 1 "head" out of 5 (not useful)
There are 6 outcomes with at least 3 "heads" out of 5 (in bold above), out of a total of 15 outcomes. Therefore, the probability is 6/15, which simplifies to 2/5.
So the answer is A. three-eighths (which is equivalent to 2/5).
Reflect on your experience in this course. You may want to think about specific concepts in math, or perhaps your habits for learning or studying math. Tell two ways you have experienced success so far. State two areas in which you can improve. Give details.
As an AI language model, I don't have experiences. However, I can provide a general response to this question based on common student experiences.
Two ways that a student may experience success in a math course is by regularly attending and actively participating in class and consistently completing assignments on time. Additionally, seeking help from the instructor or a tutor when needed can be extremely beneficial in mastering difficult concepts.
On the other hand, two areas in which a student may need improvement can be their study habits and problem-solving skills. Poor study habits such as procrastination or lack of organization can hinder a student's ability to effectively learn and apply math concepts. Additionally, improving problem-solving skills can involve practicing with various types of problems, breaking them down into smaller parts, and seeking help when needed. Developing a growth mindset and embracing mistakes as opportunities for learning can also be helpful in improving problem-solving skills.
Jacob mixes the letters J, K, L, J, K, M, N, and P thoroughly. Without looking, Terry draws one letter. Expressed as a fraction, decimal, and percentage, what is the probability that K will not be the letter Terry selects?
A. one-fourth, 0.25, 25%
B. three-fourths, 0.75, 75%
C. Start Fraction 4 over 3 End Fraction, 1.33%, 13.3%
D. start fraction 5 over 8 end fraction, 0.625, 62.5%
To find the probability of tossing "heads" at least three times out of five using the given random number table, you can count the number of outcomes that meet the criteria and divide it by the total number of possible outcomes.
Looking at the table, we can count how many times "odd" digits (representing "heads") appear at least three times out of five. Let's count:
- Row 1: 32766 -> 3 odd digits (heads)
- Row 2: 53855 -> 4 odd digits (heads)
- Row 3: 34591 -> 4 odd digits (heads)
- Row 4: 27732 -> 3 odd digits (heads)
- Row 5: 47406 -> 2 odd digits (heads)
- Row 6: 31022 -> 2 odd digits (heads)
- Row 7: 25144 -> 3 odd digits (heads)
- Row 8: 72662 -> 3 odd digits (heads)
- Row 9: 03087 -> 2 odd digits (heads)
- Row 10: 35521 -> 3 odd digits (heads)
- Row 11: 26658 -> 3 odd digits (heads)
- Row 12: 81704 -> 2 odd digits (heads)
- Row 13: 56212 -> 3 odd digits (heads)
- Row 14: 72345 -> 4 odd digits (heads)
- Row 15: 44019 -> 3 odd digits (heads)
- Row 16: 65311 -> 4 odd digits (heads)
Counting these outcomes, you can see that there are 5 outcomes (rows 2, 3, 14, 15, 16) out of the 16 possible outcomes where "heads" appears at least three times.
Therefore, the probability of tossing "heads" at least three times out of five is 5/16.
So, the correct answer is C. five-sixteenths.
To find the probability of getting "heads" at least three times out of five, we will count the number of rows that have "heads" occurring three, four, or five times.
Looking at the given random number table, we can see that "heads" is represented by odd digits (1, 3, 5, 7, 9), and "tails" is represented by even digits (0, 2, 4, 6, 8).
Let's go through each row and count the number of "heads" (odd digits):
32766 (2 heads)
53855 (3 heads)
34591 (3 heads)
27732 (4 heads)
47406 (1 head)
31022 (2 heads)
25144 (2 heads)
72662 (3 heads)
03087 (3 heads)
35521 (4 heads)
26658 (3 heads)
81704 (0 heads)
56212 (2 heads)
72345 (3 heads)
44019 (3 heads)
65311 (4 heads)
Out of the 15 rows, we can see that there are 9 rows (rows 2, 3, 4, 7, 8, 9, 10, 13, and 15) where "heads" occurs at least three times.
Therefore, the probability of getting "heads" at least three times out of five is 9/15, which can be simplified to 3/5.
So, the correct answer is A. Three-eighths.