Question

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

Statement (1): Probability of not getting the prize \[=1-\frac{20}{45}\].

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

Options

• Both the statements are true.

• Both the statements are false.

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

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

Answer 1

Both the statements are true.

Explanation: 

Given, tickets = 20 prizes and 25 blanks

total tickets = 20 + 25 = 45

By formula; the probability of an event = \[\frac{\text{Number of favourable outcomes}}{\text{Total number of possible outcomes}}\]

P(getting prize) = \[\frac{20}{45}\]

P(blank) = \[\frac{25}{45}\]

P(getting prize) + P(blank) = \[\frac{20}{45} + \frac{25}{45}\]

\[{} = \frac{20 + 25}{45}\]

\[{} = \frac{45}{45}\]

\[{} = 1.\]

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

So, statement 2 is true.

⇒ P(blank) = 1 − P(getting prize)

⇒ P(blank) = \[1 - \frac{20}{45}\]

We know that,

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

So, statement 1 is true.

∴ Both the statements are true.