Question

Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y. Make a table to show the values of the random variable.

Answer 1

SInce 3 coins are tossed and on any of coins could occur both head and tail, then Y = {0, 1, 2, 3}. Since the probability of getting a tail is equal for every coin and equals to 0.5, then Y~BIN(3, 0.5)

$P(Y=0)={3 \choose 0}*0.5^3=0.125$

$P(Y=1)={3 \choose 1}*0.5^3=0.375$

$P(Y=2)={3 \choose 2}*0.5^3=0.375$

$P(Y=3)={3 \choose 3}*0.5^3=0.125$