On a science quiz, David got 45 out of 70 items correct. What is the empirical probability of his incorrect responses? Write your answer in the simplest form of a fraction.
To find the empirical probability of David's incorrect responses, we need to subtract the number of correct responses from the total number of items and then divide by the total number of items:
Number of incorrect responses = 70 - 45 = 25
Empirical probability of incorrect responses = Number of incorrect responses / Total number of items = 25/70
To simplify this fraction, we can divide the numerator and denominator by 5:
Empirical probability of incorrect responses = (25/5) / (70/5) = 5/14
Therefore, the empirical probability of David's incorrect responses is 5/14.
To find the relative frequency of Hazel's T-shirts, we need to divide the number of T-shirts by the total number of tops (T-shirts + short sleeve blouses):
Total number of tops = 15 + 10 = 25
Relative frequency of T-shirts = Number of T-shirts / Total number of tops = 15/25
To simplify this fraction, we can divide both the numerator and denominator by 5:
Relative frequency of T-shirts = (15/5) / (25/5) = 3/5
Therefore, the relative frequency of Hazel's T-shirts is 0.6 when written in decimal form.
Each roll of the number cube is independent, so the probability of rolling an even number on any given roll is 1/2 (since there are three even numbers and three odd numbers on a standard six-sided number cube).
The expected number of times to roll an even number is equal to the probability of rolling an even number on any given roll times the number of rolls:
Expected number of times to roll an even number = Probability of rolling an even number on any given roll x Number of rolls
= 1/2 x 30
= 15
Therefore, we expect to roll an even number 15 times out of 30 rolls.
Experimental probability is the ratio of the number of times an event occurred to the total number of trials or observations. In this case, the event is someone's favorite activity being sledding, and the total number of respondents is 150.
Experimental probability of someone's favorite activity being sledding = Number of people whose favorite activity is sledding / Total number of respondents
= 40/150
To simplify this fraction, we can divide both the numerator and denominator by 10:
Experimental probability of someone's favorite activity being sledding = (40/10) / (150/10) = 4/15
Therefore, the experimental probability of someone's favorite activity being sledding is 4/15.
A six sided number cube is to be rolled 30 times. How many times do you expect to roll on an even number?
Hazel has 15 T-shirts and 10 short sleeve blouses in her wardrobe. What is the relative frequency of her T-shirts? Write your answer in decimal form.
A survey was conducted with 150 respondents that asked about their favorite activities during winter. There were 30 people who favorite building a snowman, 80 people who like skiing, and 40 who preferred sledding. What is the experimental probability that someone's favorite activity is sledding? Write your answer in simplest form of fraction..
A Calculator manufacturing company checks 500 calculator units, and 25 of them have non-functioning keys. Approximate the relative frequency of a non-defective unit from this batch of items. Express your answer in the simplest form of a fraction.
The relative frequency of a non-defective unit is equal to the number of non-defective units divided by the total number of units checked.
Since there were 25 defective units out of 500 checked, the number of non-defective units is:
500 - 25 = 475
So the relative frequency of a non-defective unit is:
475/500
To simplify this fraction, we can divide both the numerator and denominator by 25:
475/500 = (19 × 25) / (20 × 25) = 19/20
Therefore, the relative frequency of a non-defective unit from this batch of 500 calculator units is 19/20.