Experimental vs. Theoretical (7.6I)
A coin is flipped 20 times and lands on heads 12 times. What is the experimental probability of landing on tails?
What is 0.4 (or 40%).
Logic: 20 - 12 = 8 tails. 8/20 = 4/10 = 0.4.
If the theoretical probability of a spinner landing on Green is 1/5, how many times should it land on Green in 100 spins?
What is 20 times.
Logic: 1/5 \times 100 = 20
You roll a 6-sided die and flip a coin. How many total outcomes are possible?
What is 12 outcomes.
Logic: 6 (die) x 2 (coin) = 12
A bag has 10 marbles. 2 are red. What is the likelihood of picking a red marble: Likely, Unlikely, or Certain?
What is Unlikely.
Logic: 2/10 is 20%, which is less than half.
Bag A is 1/4 red. Bag B is 30% red. Which is more likely to yield a red marble?
Bag B
Logic: 30% > 25%
A bag contains 4 red, 6 blue, and 5 yellow marbles. What is the theoretical probability of not picking blue?
What is 3/5 (or 0.6).
Logic: Total is 15. Not blue is 4 + 5 = 9.
9/15 = 3/5
A survey shows 4 out of 10 students prefer soccer. In a school of 450, how many are predicted to prefer soccer?
What is 180 students.
Logic: 4/10 = x/450 --> 0.4 x 450 = 180
Create a tree diagram for flipping a coin twice. What is the probability of getting "Heads" then "Tails"?
What is 1/4 (or 0.25).
Sample space: HH, HT, TH, TT. Only 1 HT exists.
A spinner has 4 equal sections. After 20 spins, it hits Red 10 times. How many more times did it hit Red than expected?
What is 5 times.
Logic: Expected was 5 (1/4 of 20).
Experimental was 10.
10 - 5 = 5
Describe the likelihood of rolling a number less than 7 on a standard 6-sided die.
What is Certain
Logic: all numbers 1-6 are less than 7
In an experiment, a 6-sided die was rolled. The number 4 appeared 9 times in 54 rolls. Compare the experimental to the theoretical probability.
What is They are equal.
Logic: Theoretical is 1/6. Experimental is 9/54, which simplifies to 1/6
A factory finds 3 defective bulbs in every 150. If they produce 2,000 bulbs, how many are expected to be defective?
What is 40 bulbs.
Logic: 3/150 = x/2000 -->1/50 = x/2000
What is the probability of rolling a number greater than 4 on a die AND flipping "Heads" on a coin?
What is 1/6.
Logic: P(>4) = 2/6 = 1/3.
P(H) = 1/2.
1/3 x 1/2 = 1/6.
Store A has a 1/4 failure rate. Store B has a 20% failure rate. Which store is qualitatively more reliable?
What is Store B.
Logic: Store A is 25%. Store B is 20%. Lower failure rate is better.
Game X has a 2/5 win rate. Game Y has a 3/8 win rate. Which game is quantitatively better?
What is Game X
Logic: 0.4 > 0.375.
A spinner has 3 sections. P(Red) = 1/2 and P(Blue) = 1/3. What is the theoretical probability of the third section (Green)?
What is 1/6.
Logic: 1 - (1/2 + 1/3) = 1 - 5/6 = 1/6
Based on a sample where 8 out of 25 people own a dog, how many people in a city of 10,000 would be expected to own a dog?
What is 3,200 people.
Logic: 8/25 = x/10,000 --> 8 x 400 = 3,200
If you have 2 shirts and 4 pants, how many unique outfits can you make? Draw the sample space.
What is 8 outfits.
Logic: 2 x 4 = 8
P(A) = 1/3 and P(B) = 1/4. If these are independent, what is P(A and B)?
What is 1/12
Logic: (1/3 x 1/4)
If the theoretical probability is 25% but the experimental is 35%, which is "more likely"?
The experimental result is currently more likely based on the specific data provided