statistics

Question

Suppose I toss four pennies. Let X be the total number of heads showing on all pennies. 

How do I find the probability distribution of X? 

Answer 1

I don't know if this is the one you're looking for but there is formula:

 

P(x) = _nC_x * p^x * q^n-x

 

P(x) = probability that x successes will occur in n trials

n = no. of trials

x = no. of successes (that you want)

C = number of combination 

p = the probability of a success in each trial

q = the probability of a failure in each trial

 

You have 4 pennies to toss so you have 4 trials.

You want 4 pennies to be all heads (in this problem, heads = success) so you also have 4 successes.

Lastly, how many ways will there be 4 heads in 4 toss coins, obviously there's only 1 or mathematically (₄C₄ = 1).

The probability of a head (success) in each toss coin is of course, 1/2. The same as the probability of failure (tails).

 

Inserting everything:

 

P = ₄C₄ * (1/2)⁴ * (1/2)⁰

 

P = 1/16