An unbiased coin is tossed. If the outcome is | vedclass

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(C) Let $H$ be the event of getting a head and $T$ be the event of getting a tail. $P(H) = \frac{1}{2}$ and $P(T) = \frac{1}{2}$.Case $1$: If head occ

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$\frac{19}{72}$

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(C) Let $H$ be the event of getting a head and $T$ be the event of getting a tail. $P(H) = \frac{1}{2}$ and $P(T) = \frac{1}{2}$.Case $1$: If head occurs,two dice are rolled. The sum can be $7$ or $8$. The pairs for sum $7$ are $(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)$ ($6$ outcomes) and for sum $8$ are $(2,6), (3,5), (4,4), (5,3), (6,2)$ ($5$ outcomes). Total outcomes = $36$.$P(7 	ext{ or } 8 | H) = \frac{6+5}{36} = \frac{11}{36}$.Case $2$: If tail occurs,a card is picked from $9$ cards. The favorable numbers are $7$ and $8$.$P(7 	ext{ or } 8 | T) = \frac{2}{9}$.Total probability $P(7 	ext{ or } 8) = P(H) 	imes P(7 	ext{ or } 8 | H) + P(T) 	imes P(7 	ext{ or } 8 | T)$$= \frac{1}{2} 	imes \frac{11}{36} + \frac{1}{2} 	imes \frac{2}{9} = \frac{11}{72} + \frac{1}{9} = \frac{11+8}{72} = \frac{19}{72}$.

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