problem 6

Let $H$ be the event that $7$ tosses of a coin land Heads. Let $A$ be the event that a randomly selected coin is double-headed.

P (A ∣ ∣ ∣ ∣ ∣ H) = \frac{P (A) P (H | A)}{P (A) P (H | A) + P (A^{c}) P (H | A^{c})} = \frac{\frac{1}{100}}{\frac{1}{100} + \frac{99}{100} * {(\frac{1}{2})}^{7}}