There are two coins, say blue and red. For blue coin, probability of getting head is 0.99 and for red coin, it is 0.01. One coin is chosen randomly and is tossed. The probability of getting head is
We have two coins: - Blue coin: \(P(H|B)=0.99\). - Red coin: \(P(H|R)=0.01\). One coin is chosen at random, so \[ P(B)=P(R)=\tfrac{1}{2}. \] By the law of total probability: \[ P(H)=P(B)\cdot P(H|B)+P(R)\cdot P(H|R). \] \[ P(H)=\tfrac{1}{2}(0.99)+\tfrac{1}{2}(0.01). \] \[ P(H)=\tfrac{0.99+0.01}{2}=\tfrac{1}{2}=0.5. \] \[ \boxed{0.5} \]
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