Out of 50 tickets numbered 00, 01, 02, …, 49, one ticket is drawn randomly. The probability that the ticket has the product of its digits 7, given that the sum of the digits is 8, is

Question

The distribution function $ F(X) $ of a discrete random variable $ X $ is given. Then $ P[X = 4] + P[X = 5] $:
\[ \begin{array}{|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline F(X = x) & 0.2 & 0.37 & 0.48 & 0.62 & 0.85 & 1 \\ \hline \end{array} \]

Answer 1

Understanding the Concept: Conditional probability = Favorable Total (given condition)

Step 1: Condition: sum of digits = 8.
Possible pairs (tens, units): \[ (0,8),(1,7),(2,6),(3,5),(4,4) \]

Step 2: Total outcomes = 5.

Step 3: Product = 7 only for: \[ (1,7) \]

Step 4: Favorable outcomes = 1.

Step 5: Probability: \[ P = \frac{1}{5} \] Final Answer:
Answer = $\frac{1}{5}$

Out of 50 tickets numbered 00, 01, 02, …, 49, one ticket is drawn randomly. The probability that the ticket has the product of its digits 7, given that the sum of the digits is 8, is

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The Correct Option is C

Solution and Explanation

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