Question:
An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered \(1,2,3,\ldots,9\) is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is :
An unbiased coin is tossed. If the outcome is a head then a pair of unbiased dice is rolled and the sum of the numbers obtained on them is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered \(1,2,3,\ldots,9\) is randomly picked and the number on the card is noted. The probability that the noted number is either 7 or 8 is :
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Use total probability: P(head)P(7 or 8 | dice) + P(tail)P(7 or 8 | card).
Updated On: Nov 5, 2026
- \(\frac{19}{36}\)
- \(\frac{15}{72}\)
- \(\frac{13}{36}\)
- \(\frac{19}{72}\)
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The Correct Option is D
Solution and Explanation
Head (prob. \(\frac12\)): sum 7 occurs in 6 ways and sum 8 in 5 ways out of 36, so P \(=\frac{11}{36}\).
Tail (prob. \(\frac12\)): card 7 or 8 out of nine cards: P \(=\frac29\).
Total \(=\frac12\cdot\frac{11}{36}+\frac12\cdot\frac29=\frac{11}{72}+\frac{8}{72}=\frac{19}{72}\).
Answer: (4) \(\frac{19}{72}\)
Tail (prob. \(\frac12\)): card 7 or 8 out of nine cards: P \(=\frac29\).
Total \(=\frac12\cdot\frac{11}{36}+\frac12\cdot\frac29=\frac{11}{72}+\frac{8}{72}=\frac{19}{72}\).
Answer: (4) \(\frac{19}{72}\)
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