JEE Mains · Maths · STD 11 - 14. probability
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 the is noted. If the toss of the coin results in tail then a card from a well-shuffled pack of nine cards numbered \(1, 2, 3,….., 9\) is randomly picked and the number on the card is noted. The probability that the noted number is either \(7\) or \(8\) is
- A \(\frac{{13}}{{36}}\)
- B \(\frac{{15}}{{72}}\)
- C \(\frac{{19}}{{72}}\)
- D \(\frac{{19}}{{36}}\)
Answer & Solution
Correct Answer
(C) \(\frac{{19}}{{72}}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{P}(7 \text { or } 8)\) \(=P(H) P(7 \text { or } 8)+P(T) P(7 \text { or } 8)\) \(=\frac{1}{2} \times \frac{11}{36}+\frac{1}{2} \times \frac{2}{9}=\frac{11}{72}+\frac{1}{9}=\frac{19}{72}\)
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