NDA 2024
- Exam
- NDA
- Year
- 2024
- Subject
- Mathematics
- Chapter
- Probability
NDA 2024 · Mathematics · Probability
A fair coin is tossed till two heads occur in succession. What is...
A fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6 ?
Options
- A
- B
- C
- D
Correct answer
B.
Step-by-step solution
Fair coin is tossed till two heads occur in succession.
(the number of tosses required in less than 6 ) \left(\frac{1}{2}\right)^5\frac{=\left(\frac{1}{2}\right)^2\left[1-\left(\frac{1}{2}\right)^4\right]}{1-\frac{1}{2}}=\frac{\frac{1}{4}\left(1-\frac{1}{16}\right)}{\frac{1}{2}}=\frac{1}{2}\left(\frac{15}{16}\right)=\frac{15}{32}