Problem of the Day

An unfair coin comes up heads 60% of the time and tails 40% of the time when it is tossed. What is the probability of getting exactly three heads on five tosses of this coin?

A. \displaystyle \frac{10}{32}

B. \displaystyle \frac{27}{125}

C. \displaystyle \frac{2^33^3}{5^5}

D. \displaystyle \frac{3}{5}

E. \displaystyle \frac{6^3}{5^4}


Reveal Answer



E. $\displaystyle \frac{6^3}{5^4}$

See the Solution



Consider one possible successful sequence: HHHTT. Each toss has a $\frac{3}{5}$ probability of being heads and a $\frac{2}{5}$ probability of being tails. Thus, this sequence will occur with probability $(\frac{3}{5})^3\cdot(\frac{2}{5})^2$. However, this is only one of many possible successful sequences. To determine the total number of sequences, note that there are 5 tosses and the two tails can be assigned to any of those five tosses in $_5C_2=10$ ways. Thus, the overall probability is $10\cdot(\frac{3}{5})^3\cdot(\frac{2}{5})^2$.





Comments are closed.