Number of Heads

[nycmathguy]

Toss a coin 100 times, how many Heads will come up?

Let me see.

A coin has two sides.

If I toss the coin 100 times, the probability of Heads is 1/2 for each toss.

So, for 100 toses, each toss has a 1/2 chance of being Heads.

I say, 100 • 1/2 = 50.

Answer: 50 times

Yes?

 

[MathLover1]

The probabilities of each event - Heads and Tails - are both equal.

 

[nycmathguy]

The probabilities of each event - Heads and Tails - are both equal.

Both equal meaning 1/2 for each side of the coin.

 

[Country Boy]

What you are trying to do is correct but your wording is poor.

"Toss a coin 100 times, how many Heads will come up?"
"Answer: 50 times"

Grammatically, that says that if you flip a coin 100 times, it is sure to come up heads exactly 50 times, which is not true!

What is true is that if you do this trial, flipping a coin 100 times, repeatedly, it will come up heads on each trial an average of 50 times. It could do that without ever coming up heads exactly 50 times. The 'expected number' of heads on any one trial is 50.

What is true for each flip is that on each experiment the probability the coin will come up heads "n" time is (n!(100- n)!))/(2^100)(100!). The probability that you get exactly 50 heads in 100 flips is (50!(50!))/(2^100)(100!) which is very, very small, about 7.82 x 10^(-60).

 

[nycmathguy]

What you are trying to do is correct but your wording is poor.

"Toss a coin 100 times, how many Heads will come up?"
"Answer: 50 times"

Grammatically, that says that if you flip a coin 100 times, it is sure to come up heads exactly 50 times, which is not true!

What is true is that if you do this trial, flipping a coin 100 times, repeatedly, it will come up heads on each trial an average of 50 times. It could do that without ever coming up heads exactly 50 times. The 'expected number' of heads on any one trial is 50.

What is true for each flip is that on each experiment the probability the coin will come up heads "n" time is (n!(100- n)!))/(2^100)(100!). The probability that you get exactly 50 heads in 100 flips is (50!(50!))/(2^100)(100!) which is very, very small, about 7.82 x 10^(-60).

I plan to study probability after calculus.