Binomial Distribution Flashcards - GRE Subject Test: Math

This problem uses the Binomial Distribution: $\binom{n}{k}p^k(1-p)^{n-k}$

For this problem n is the number of trials, or 15. Because the problem stated that the coin was a fair coin the probability of heads is one half, or .5.

The binomial distribution is a discrete distribution so the expression x<3 has to be broken down.

$Pr(x=0)=\begin{pmatrix} 15\0 \end{pmatrix} (.5)^0(1-.5)^{15}=.000031$

$Pr(x=1)=\begin{pmatrix} 15\1 \end{pmatrix} (.5)^1(1-.5)^{14}=.00046$

$Pr(x=2)=\begin{pmatrix} 15\2 \end{pmatrix} (.5)^2(1-.5)^{13}=.0032$

Adding the probabilities will give the final answer.

Binomial Distribution - GRE Subject Test: Math

A fair coin is tossed 15 times. What is the probability of observing less than 3 heads?