NDA2024MathematicsProbabilityActual
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
- A5 64
- B15 32
- C31 64
- D19 32
Correct answer
B. 15 32
Step-by-step solution
Fair coin is tossed till two heads occur in succession. P (the number of tosses required in less than 6 ) = P ( HH )+ P ( THH )+ P ( TTHH )+ P ( TTTHH )= ( 1 2 )^2+ ( 1 2 )^3+ ( 1 2 )^4+ ( 1 2 )^5 = ( 1 2 )^2 [1- ( 1 2 )^4 ] 1- 1 2 = 1 4 (1- 1 16 ) 1 2 = 1 2 ( 15 16 )= 15 32