Question

The probability is $\frac{1}{2}$ that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times, what is the probability that on at least one of the tosses the coin will turn up tails?

• A. $\frac{1}{8}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $\frac{7}{8}$
• E. $\frac{15}{16}$

Answer 1

The correct option is D $\frac{7}{8}$

The probability is $\frac{1}{2}$ that a certain coin will turn up heads on any given toss. If the coin is to be tossed three times,the probability that on at least one of the tosses the coin will turn up tails

To get at least 1 tails, you can get one of the 3 configurations (in no particular order):

$HHT->3\ast {\frac{1}{2}}^3$

$HTT->3\ast {\frac{1}{2}}^3$

$TTT->{\frac{1}{2}}^3$

$P=\frac{3}{8}+\frac{3}{8}+\frac{1}{8}=\frac{7}{8}$