Question

drawing a 1, 2, or 3 from 9 cards numbered 1-9, replacing the card,
and drawing a 7, 8, or 9
1/3
3/8
C
1/9
d
1/12​

Answer 1

Answer:

The required probability is option $C)\ \dfrac{1}{9}$

Step-by-step explanation:

There are a total of 9 cards.

Total number of cases = 9

Let A be the event of choosing 1, 2 or 3.

Total number of favorable cases for event A = 3

Let B be the event of choosing 7, 8 or 9.

Total number of favorable cases for event B = 3

Formula for finding probability of an event E is:

$P(E) = \dfrac{\text{Number of favorable cases}}{\text {Total number of cases}}$

Finding P(A), using the formula:

$P(A) = \dfrac{3}{9}\\\Rightarrow \dfrac{1}{3}$

Now, it is given that the card is replaced, so again total number of cases are 9.

For finding P(B), using the formula:

$P(B) = \dfrac{3}{9}\\\Rightarrow \dfrac{1}{3}$

To find the probability that events A and B both happen, we can simply multiply P(A) and P(B) because these are independent events.

$\text{Required probability = }P(A) \times P(B)\\\Rightarrow \dfrac{1}{3} \times \dfrac{1}{3} \\\dfrac{1}{9}$