For this activity, you will need two different coins. First, you will determine the theoretical probability of events. Then, you will flip the coins 100 times and determine the experimental probability of the events. Flip two different coins 100 times, and record the results of each coin toss in a table like the one below:

Result Frequency
Two heads
Two tails
One head, one tail
Answer the following questions based on the data you gathered. You must show your work to receive credit.

What is the theoretical probability that a coin toss results in two heads showing?
What is the experimental probability that a coin toss results in two heads showing?
What is the theoretical probability that a coin toss results in two tails showing?
What is the experimental probability that a coin toss results in two tails showing?
What is the theoretical probability that a coin toss results in one head and one tail showing?
What is the experimental probability that a coin toss results in one head and one tail showing?
Compare the theoretical probabilities to your experimental probabilities. Why might there be a difference?

Step-by-step explanation:

for the theoretical probability, it doesn't matter if you flip 100 coins or 10000 coins because it is a theory behind probability.

Probability of Event P(E) = No. of. Favourable outcomes/ No. of. Possible outcomes.

The experimental probability will get closer to the theoretical probability the more coins you flip. This means that if you flip an infinite number of coins, you will get theoretical probability.

There are four possibilities.

H-H

H-T

T-H

T-T

Therefore, there is 1/4 chance to get two heads 25%.

There is 2/4 or 1/2 chance to get one heads and one tails 50%

And there is also 1/4 chance to get two tails 25%.

The experimental probability of tossing 2 coins 100 times is useless and a waste of time. Just make up some numbers that make sense and are close to the theoretical probability.

For example

H-H 31 times  31%

T-T 23 times 23%

One H and One T 46 times 46%

The variation between theoretical and Experimental is because you only flipped the coins 100 times. Theoretical probability does not account for this.

d. bc = 12 and ef = 16

step-by-step explanation:

we are given that δabc : δdef such that .

also, it is given that

so, from the options, we need that .

a.

b.

c.  

d.

as, we can see that only option d gives the same ratio as i.e. .

hence, the possible lengths are bc = 12 and ef = 16.

we need the options

step-by-step explanation: