Question

With one hand, three coins are tossed simultaneously until a toss of 100 tosses, What is the number of ways of getting combinations having:

1) three heads
2) two heads and one tail
3) one head and two tails
4) three tails

show the probability of each combination, show the expected frequency.

Answer 1

@biocrystal

Answer 2

There's only one way to get three heads - one head per coin. That is, \(\dbinom33=1\).

Two heads can be counted similarly: \(\dbinom32=3\).

One head: \(\dbinom31=3\).

Three tails (i.e. zero heads): \(\dbinom30=1\).

Answer 3

regarding the (two heads,one tail) and (one head and two tails)..what is the number of its outcome? im confuse

Answer 4

Of the three coins, you want a toss to contain 2 heads. This is computed as a binomial coefficient (or combination). If the notation is unfamiliar to you, I mean
\[\large{}_nC_r=\binom nr=\frac{n!}{r!(n-r)!}\]

Answer 5

I'm already familiar what the binomial coefficent formula..whats the significance of 100 tosses??

Answer 6

That comes into play when you're computing the frequency. A frequency is the actual number of times a certain combination will show up in 100 tosses.

So say you get 0.5 as one of the probabilities. Then 50 (half of 100) is the frequency of the combination.

Answer 7

how to compute the porbabilities? :D

Answer 8

How many total outcomes can you have? With two sides per coin, and three coins, that gives you \(2^3=8\) total possibilities. (Notice that you could also count this by adding up the other outcomes - every possibility is listed.)

The probability of the first event is 1/8, since there's only one desired outcome (three heads) of the total possible.

Answer 9

thanks for helping me :)) big hugs!!

Answer 10

You're welcome!