Question

FAN AND MEDAL

Answer 1

you will need two 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 coins 100 times, and record the results of each coin toss in a table like the one below:

Answer 2

Result Frequency
Two heads lllll lllll lllll lllll lllll ll
Two tails lllll lllll lllll lllll lllll l
One head, one tail lllll lllll lllll lllll lllll lllll lllll lllll lllll ll

Answer 3

1. What is the theoretical probability that a coin toss results in two heads showing?

Answer 4

3. What is the theoretical probability that a coin toss results in two tails showing?

Answer 5

5. What is the theoretical probability that a coin toss results in one head and one tail showing?

Answer 6

what is the probability of getting heads for 1 toss of a coin ?

Answer 7

50%

Answer 8

now flip it again. it's 1/2 or 0.5 chance of getting a second head
if the events are independent (which means the first flip does not affect the second flip),
you multiply the two probabilities. 1/2 * 1/2 = ?

Answer 9

100%

Answer 10

idk

Answer 11

2/2

Answer 12

are you saying you can't multiply
\[ \frac{1}{2} \cdot \frac{1}{2} \]
?

Answer 13

to mult fractions, top*top divided by bottom * bottom

Answer 14

or if you write 1/2 as a decimal 0.5
0.5 * 0.5

Answer 15

so it is 0.25

Answer 16

yes, the theoretical chance of getting 2 heads is 1/4 or 0.25
by the same reasoning that is also the theoretical prob of getting 2 tails

Answer 17

okay so it's 2/4 or 0.50 chance for getting head and tails right?

Answer 18

yes. there are a few ways to figure it:
if 0.25 for two heads and 0.25 for two tails and xx for h /t
and it has to add up to 1 (or 100%)
we have
0.25+0.25+x = 1
0.5 + x = 1
x= 1-0.5
x=0.5
i.e. 1/2 chance of getting a head and a tail (in any order)

Answer 19

the other way is to say
1/2 chance of getting a T. then on the 2nd flip 1/2 chance of getting H
so 1/2 *1/2 = 1/4 chance for getting TH

also
1/2 chance of first getting H, then 1/2 for T
and 1/4 chance for getting HT
so the chance of TH or HT is 1/4+1/4 = 1/2

Answer 20

thanks so much

Answer 21

your "flip experiment" should get something close to
25 heads
25 tails
50 head/tail

Answer 22

i got the answer for that i got 27, 26 and 47

Answer 23

yes, those numbers are close to the theoretical, and are reasonable.

Answer 24

thanks so much for your help :)

Answer 25

yw