Question:
In a lottery containing \(35\) tickets, exactly \(10\) tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is
In a lottery containing \(35\) tickets, exactly \(10\) tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is
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Probability is calculated as \(\dfrac{\text{Favourable outcomes}}{\text{Total outcomes}}\). For “not getting” an event, count the complementary outcomes.
Updated On: Jun 15, 2026
- \(\dfrac{1}{10}\)
- \(\dfrac{2}{5}\)
- \(\dfrac{2}{7}\)
- \(\dfrac{5}{7}\)
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The Correct Option is D
Solution and Explanation
Step 1: Find the total number of tickets.
Total number of tickets in the lottery is
\[ 35 \]
Out of these, \(10\) tickets bear a prize.
Step 2: Find the number of tickets without prize.
Number of tickets that do not bear a prize is
\[ 35-10 \]
\[ =25 \]
Step 3: Use the probability formula.
Probability of not getting a prize is
\[ \frac{\text{Number of non-prize tickets}}{\text{Total number of tickets}} \]
Therefore,
\[ P(\text{not getting a prize}) = \frac{25}{35} \]
\[ =\frac57 \]
Step 4: Final conclusion.
Hence, the required probability is
\[ \boxed{\frac57} \]
Total number of tickets in the lottery is
\[ 35 \]
Out of these, \(10\) tickets bear a prize.
Step 2: Find the number of tickets without prize.
Number of tickets that do not bear a prize is
\[ 35-10 \]
\[ =25 \]
Step 3: Use the probability formula.
Probability of not getting a prize is
\[ \frac{\text{Number of non-prize tickets}}{\text{Total number of tickets}} \]
Therefore,
\[ P(\text{not getting a prize}) = \frac{25}{35} \]
\[ =\frac57 \]
Step 4: Final conclusion.
Hence, the required probability is
\[ \boxed{\frac57} \]
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