Answer to Question #253960 in Statistics and Probability for ligaya

Question

6 coins are tossed. Let Z be the random variable representing the number of heads that occur. What are the values of the random variables?

Answer 1

If 6 coins are tossed, there are 7 possabilities of amount of the heads: from 0 to 6

So, Z could take any of these values.

Z~Bin(0.5, 6)

$P(Z=k)={n \choose k}*p^{k}*(1-p)^{n-k}$ , where p is the probability of succes(0.5 in this case), n is the amount of experiments(6 in this case)

Since p = 1-p = 0.5, the formula above can be simplified

$P(Z=k)={6 \choose k}*0.5^{6}$

After calculation of all the probabilities for k from 0 to 6, we can build the table with the probability values

Rounded to 3 decimal