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A box contains 55 flash cards showing different numbers on it. If a card is picked up at random from the box, the probability of getting an even number is $111 .$ How many cards have odd numbers written on it?

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answer is B.

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Detailed Solution

Given that the probability of getting an even number from the box of 55 flash cards is

111 .

We need to find out how many cards have odd numbers written on it.
Probability of an event E is defined as:

P (E) = \frac{Number of favorable outcomes}{Total number of possible outcomes}

There are 55 flash cards in the box, therefore the total number of possible outcomes will be 55.
Let us assume the box contain

x

cards having odd numbers and

n

cards having even numbers.
Let

E

be the event of getting an even number card.
From question we have,

P (E) = 111

Now, we know that probability of getting an even card is given by:

P (E) = n 55

Equating both the equations, we get,

111 = n 55 ⇒ 55 = 11 n ⇒ n = 5511 ⇒ n = 5

Even cards in the box are 5.
We know that,
Even cards + Odd cards = Total cards in the box
Therefore, we have,

5 + x = 55 ⇒ x = 55 − 5 ⇒ x = 50

Hence, 50 cards have odd numbers written on it.
Therefore, option 2 is correct.

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