Question

Two persons A and B toss a coin 50 times each together. Find the probability both of them get tails at the same time.

• A. ${\left(\frac{1}{2}\right)}^{50}$
• B. ${\left(\frac{1}{4}\right)}^{100}$
• C. ${\left(\frac{1}{4}\right)}^{50}$
• D. ${\left(\frac{1}{3}\right)}^{50}$

Answer 1

Answer: (C)

${\left(\frac{1}{4}\right)}^{50}$

When A and B toss a coin, the sample space is $\{HH,HT,TH,TT\}$
So the probability of getting tail on both coins $=\frac{1}{4}$
Hence the required probability in 50 trials = $\frac{1}{4},\frac{1}{4}...50times={\left(\frac{1}{4}\right)}^{50}$