Question

A group of students was surveyed in a middle school class. They were asked how many hours they work on math homework each week. The results from the survey were recorded.

Number of Hours Total Number of Students
0 1
1 8
2 2
3 5
4 9
5 7
6 3


Determine the probability that a student studied for exactly 1 hour. Round to the nearest hundredth.
0.03
0.23
0.30
0.77
Question 15(Multiple Choice Worth 2 points)
(Experimental Probability MC)

A student randomly draws a card from a standard deck of 52 cards. He records the type of card drawn and places it back in the deck. This is repeated 20 times. The table below shows the frequency of each outcome.


Outcome Frequency
Heart 7
Spade 3
Club 6
Diamond 4


Determine the experimental probability of drawing a heart.
0.13
0.25
0.35
0.70

Answer 1

To find the probability that a student studied for exactly 1 hour, divide the number of students who studied for 1 hour by the total number surveyed, resulting in 0.23. The experimental probability of drawing a heart is determined by dividing the frequency of drawing a heart by the total draws, yielding 0.35.

Step-by-step explanation:

The probability that a student studied for exactly 1 hour can be found by dividing the number of students who studied for 1 hour by the total number of students surveyed. We calculate this by taking the number of students who studied for 1 hour (8 students) and dividing it by the sum of all students, which adds up to 35 (1 + 8 + 2 + 5 + 9 + 7 + 3). So the probability is 8/35, which when rounded to the nearest hundredth is approximately 0.23.

The experimental probability of drawing a heart from a deck of cards based on the student's experiment can be found by dividing the frequency of drawing a heart (7 times) by the total number of draws (20 times). Hence, the experimental probability is 7/20, which equals 0.35 when rounded to two decimal places.

Answer 2

For the first question, To determine the probability that a student studied for exactly 1 hour, we can use the formula:

P(X=1) = (number of students who studied for 1 hour) / (total number of students)

In this case,

P(X=1) = 8/30 = 0.27 (rounded to two decimal places)

So the probability that a student studied for exactly 1 hour is 0.27

For the second question, to determine the experimental probability of drawing a heart, we can use the formula:

P(Heart) = (number of times a heart is drawn) / (total number of draws)

In this case,

P(Heart) = 7/20 = 0.35

So the experimental probability of drawing a heart is 0.35

Therefore, the option 3 is the answer.

Step-by-step explanation: