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Suppose there are two coins. The first coin gives heads with probability $\dfrac{5}{8}$ when tossed, while the second coin gives heads with probability $\dfrac{1}{4}.$ One of the two coins is picked up at random with equal probability and tossed. What is the probability of obtaining heads ?

- $\left(\dfrac{7}{8}\right)$
- $\left(\dfrac{1}{2}\right)$
- $\left(\dfrac{7}{16}\right)$
- $\left(\dfrac{5}{32}\right)$

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**Answer is C)** $\dfrac{7}{16}$

Probability of obtaining head$= \text{Probability of picking first coin} \times \text{Probability of getting head on first coin}$

$+ \text{Probability of picking second coin}\times \text{Probability of getting head on second coin}$

$ = \left(\dfrac{1}{2}\times \dfrac{5}{8}\right) +\left( \dfrac{1}{2}\times \dfrac{1}{4}\right) = \dfrac{7}{16}.$