Question

Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn and Dawn’s results?

Answer 1

Step by step please?

Answer 2

You're looking for a probability figure based on actual experience/experimentation. Based upon the results of the girls' experiment (Lynn and Dawn tossed a coin 60 times and got heads 33 times), we can predict that if the same coin is tossed again (an independent experiment), the probability of getting a head AGAIN is simply 33/60.

You didn't ask, but if you wanted to, you could develop a confidence interval for the true proportion. But that's probably beyond the scope of the question you've shared here on OS.

Answer 3

Yay I did it right then... I wasn't sure lol it seemed too easy...

How would I go about developing a confidence interval?

Answer 4

Since this is likely to involve some concepts you may not yet have learned, I'll just go through the calculations; we could discuss this in more depth later if you're interested.

Lynn and Dawn tossed a coin 60 times and got heads 33 times. What is the experimental probability of tossing heads using Lynn and Dawn’s results?

As we've already discussed, the experimental probability of getting a head on a toss is 33/60, or 0.55. Another name that is applicable to this is "point estimate."

Then, supposing we wanted a "90% confidence interval," and choosing the "z-critical value" 1.645 (corresponding to that level of confidence), the confidence interval would be constructed like this:

\[.55 \pm 1.645\sqrt{\frac{ .55(1-.55) }{ 60 }}\]

Answer 5

which comes out to\[.55\pm1.645(0.064), \]
OR
\[.55\pm0.106\rightarrow( 0.444 ,0.656).\]

Answer 6

Here's what this means: If we repeatedly choose samples of 60 coin tosses, then roughly 90% of the time, our confidence interval will contain the true proportion of heads to number of tosses.

Since a fair coin will come up heads roughly half the time (proportion = .5), it's great to see that this 0.500 does lie within the confidence interval posted above.

Again,
.55 = experimental probability of obtaining a head
1.645: z-critical value when we're looking for a 90% confidence interval

My best to you. MM

Answer 7

What in the world... I remember when understanding probability was... simple and well... understanding. I'm so lost I'm sorry... but thank you anyways.