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Mathematics

In a lottery ticket, there are 20 prizes and 25 blanks.

Statement (1): Probability of not getting the prize = 1 - 2045\dfrac{20}{45}

Statement (2): P(getting prize) + P(blank) = 1

  1. Both the statements are true.

  2. Both the statements are false.

  3. Statement 1 is true, and statement 2 is false.

  4. Statement 1 is false, and statement 2 is true.

Probability

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Answer

Given, tickets = 20 prizes and 25 blanks

total tickets = 20 + 25 = 45

By formula; the probability of an event = Number of favourable outcomesTotal number of possible outcomes\dfrac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}

P(getting prize) = 2045\dfrac{20}{45}

P(blank) = 2545\dfrac{25}{45}

P(getting prize) + P(blank) =2045+2545=20+2545=4545=1.\text{P(getting prize) + P(blank) }= \dfrac{20}{45} + \dfrac{25}{45}\\[1em] = \dfrac{20 + 25}{45} \\[1em] = \dfrac{45}{45} \\[1em] = 1.

Thus, P(getting prize) + P(blank) = 1

So, statement 2 is true.

⇒ P(blank) = 1 - P(getting prize)

⇒ P(blank) = 1 - 2045\dfrac{20}{45}

We know that,

P(not getting the prize) = P(blank)

So, statement 1 is true.

∴ Both the statements are true.

Hence, option 1 is the correct option.

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