Question

There are 8 cards in a bag, labeled 1 through 8. You draw an even number. Without returning the card, you draw a 5. What is the probability that you draw an even number then a 5?

Answer 1

The probability that you draw an even number then a 5 is $(\frac{1}{14} )$

Step-by-step explanation:

Total number of cards in the bag = 8

The cards are numbered as {1 , 2 , 3  , 4  , 5  , 6 ,  7,  8}

Now, the total even number in the card = { 2, 4 , 6 and 8}

So, P(Drawing an ever card)  = $\frac{\textrm{The total even cards}}{\textrm{Total cards in the bag}} = \frac{4}{8} = \frac{1}{2}$

Now, the drawn card is not replaced.

So, the total cards left in the bag  = 8 - 1  = 7

The probability of drawing a card with number 5  = $\frac{\textrm{Total cards with number 5}}{\textrm{Total cards left in the bag}} = \frac{1}{7}$

⇒The combined probability  = $\frac{1}{2} \times \frac{1}{7} = (\frac{1}{14})$

Hence, the probability that you draw an even number then a 5 is $(\frac{1}{14} )$