AP EAPCET 20-Aug-2021 Shift 2 Paper

Let probability of getting head =x
Then, probability of getting tail =1−x
Tom wins if he gets head
H, TTH, TTTTH, ... (alternative through)
Probability of Tom winning game =62.5%=

625

1000

P(H)+P(TTH)+P(TTTTH)+...=

625

1000

x+(1−x)(1−x)x+(1−x)4x+...=

625

1000

⇒x[1+(1−x)2+(1−x)4+...]=

625

1000

⇒x+

1

1−(1−x)2

=

625

100

⇒

x

2x−x2

=

625

1000

⇒

1

2−x

=

625

1000

⇒x=

2

5

( probability of head )
⇒1−x=

3

5

(probability of tails)
∴ Probability of getting exactly 3 heads on tossing a coin or 5 times =‌5C3x3(1−x)2 =10×(

2

5

)3(

3

5

)2=

144

625