Question

Two cards are selected from a deck of cards numbered from 1 to 10. Once a card is selected, it is not replaced. What is P(two even numbers)? Write the answer as a fraction in simplest form.

Include Explanation please

Answer 1

10 cards would have 5 even cards.

First pick would be 5/10 = 1/2 probability of getting an even card.

Without replacing there are 9 cards left with 4 even ones. The probability of picking an even card would be 4/9

The probability of both happening would be Found by multiplying the two probability’s together:

1/2 x 4/9 = 4/18 = 2/9

Answer 2

Two cards are selected from a deck of cards numbered from $1$ to $10$ and once a card is selected, it is not replaced, then Probability of two even numbers is $\frac{2}{9}$ .

What is Probability ?

Probability is a ratio of the number of favorable outcomes to the number of possible outcomes of the experiment.

Probability$(E)$ $=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}$

We have,

Let $E$ be event of drawing cards.

A deck of cards numbered from $1$ to $10$ .

i.e. total number of possible outcomes $=10$

And,

Even numbers from $1$ to $10$  are $2,4,6,8,10$

$=10$

Total even numbers are $5$.

So,

Probability$(E)$ $=\frac{Number \ of \ favorable \ outcomes}{Number \ of \ possible \ outcomes \ of \ the \ experiment}$

Probability$(E)$ $=\frac{5}{10}*\frac{4}{9}$

                           $=\frac{2}{9}$

So, the Probability of two even numbers is $\frac{2}{9}$ , as there are total $10$ cards and it is said that once a card is selected, it is not replaced, so when one card is selected there remains only $9$ cards, so when next time we select a card then Probability will be from those $9$ cards.

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