A spinner has 8 equally sized sections labeled as A, B, C, D, E, F, G, H. In 160 spins, how many times can you expect to spin and land on a consonant?
The theoretical probability of landing on a 3 when rolling a six-sided number cube is 1/6, since there is one 3 out of six equally likely outcomes.
The experimental probability is found by the number of times the event occurred (in this case, landing on a 3) divided by the total number of trials (30 rolls).
Experimental P(3) = Number of times landing on a 3 / Total number of rolls = 10 / 30 = 1/3
Therefore:
Theoretical P(3) = 1/6
Experimental P(3) = 1/3
The answer is: 1/3.
There are 5 consonants in the sections labeled B, C, D, F, and G.
Therefore, the probability of landing on a consonant in one spin is 5/8.
To find the expected number of times to spin and land on a consonant in 160 spins, we multiply the probability of landing on a consonant in one spin by the total number of spins:
Expected number of spins = (5/8) * 160 = 100
Therefore, you can expect to spin and land on a consonant 100 times in 160 spins.
h is a constonant
Apologies for the oversight. In that case, there are 6 consonants in the sections labeled B, C, D, F, G, and H.
The probability of landing on a consonant in one spin is 6/8 = 3/4.
Expected number of spins = (3/4) * 160 = 120
Therefore, you can expect to spin and land on a consonant 120 times in 160 spins.
A six-sided number cube is rolled 30 times and lands on 3 ten times and on 5 eight times. Calculate the theoretical AND experimental probabilities of landing on a 3. Write your answer in the simplest form of a fraction.
Theoretical P(3) = _____
Experimental P(3) = _____
Options:
1/3
4/15
1/2
1/6
Charles is going to flip 3 quarters and lists the sample space in a tree diagram
How many outcomes are possible from flipping 3 quarters?
A. 1/2
B. 4
C. 8
D. 64
Which is the probability that all 3 quarters will land showing the same side?
A. 2
B. 1
C. 1/4
D. 1/8
To find the number of outcomes when flipping 3 quarters, we can use the fundamental counting principle. Since each quarter has 2 possible outcomes (heads or tails) and there are 3 quarters being flipped, the total number of outcomes is 2 * 2 * 2 = 8.
Therefore, the number of outcomes possible from flipping 3 quarters is 8, which makes option C. 8 the correct answer.
Next, let's find the probability that all 3 quarters will land showing the same side (either all heads or all tails).
There are only 2 ways in which all 3 quarters can show the same side (all heads or all tails) out of the 8 possible outcomes. So, the probability is 2 favorable outcomes out of 8 total outcomes, which simplifies to 1/4.
Therefore, the correct answer is C. 1/4.
Javon and Micah are creating a simulation. They know that approximately 20% of the students in their class have blue eyes. Which of the simulations represent a 20% chance of selecting a student with blue eyes. Select all that apply.
Options:
Placing 20 pieces of paper in a bag and 10 say blue eyes.
Placing 40 pieces of paper in a bag and 4 say blue eyes.
Placing 50 pieces of paper in a bag and 10 say blue eyes.
Placing 100 slips of paper in a bag and 20 say blue eyes.
Placing 25 slips of paper in a bag and 5 say blue eyes.
To represent a 20% chance of selecting a student with blue eyes, you would need to have 20% of the total number of pieces of paper in the bag to say blue eyes.
Let's see which simulations satisfy this condition:
1. Placing 20 pieces of paper in a bag and 10 say blue eyes. (20 pieces with 10 saying blue eyes - 50% chance)
2. Placing 40 pieces of paper in a bag and 4 say blue eyes. (40 pieces with 4 saying blue eyes - 10% chance)
3. Placing 50 pieces of paper in a bag and 10 say blue eyes. (50 pieces with 10 saying blue eyes - 20% chance)
4. Placing 100 slips of paper in a bag and 20 say blue eyes. (100 pieces with 20 saying blue eyes - 20% chance)
5. Placing 25 slips of paper in a bag and 5 say blue eyes. (25 pieces with 5 saying blue eyes - 20% chance)
The simulations that represent a 20% chance of selecting a student with blue eyes are:
- Placing 50 pieces of paper in a bag and 10 say blue eyes.
- Placing 100 slips of paper in a bag and 20 say blue eyes.
- Placing 25 slips of paper in a bag and 5 say blue eyes.
Therefore, the correct options are:
3. Placing 50 pieces of paper in a bag and 10 say blue eyes.
4. Placing 100 slips of paper in a bag and 20 say blue eyes.
5. Placing 25 slips of paper in a bag and 5 say blue eyes.