Question

A pack of cards consists of 9 cards numbered 1 to 9. Three cards are drawn at random with replacement. Then the probability of getting 1 even and 2 off numbered card is ??

Answer 1

There is a total of 3 cards taken out from the pack in a random order that will make it 3!

That will make it 3 * 2 * 1 = 6 however, we have to see how many time we can have one even and 2 off numbered card making it a 3.

Hence, the probability will be 3/6 = 1/2

Answer 2

The probability of getting 1 even and 2 odd numbered card is $\frac{100}{243}$

Step-by-step explanation:

Given Data

Total number of cards in a pack n(S) = 9

To find - the probability of getting 1 even and 2 odd number card when three cards are drawn randomly

Total number of even numbered card n(A) = 4

Total number of odd numbered card n(B) = 5

Probability P(A) of getting even numbered card is

$P(A) = \frac{n(A)}{n(S)}$

$P(A) = \frac{4}{9}$

Probability P(B) of getting odd numbered card is

$P(B) = \frac{n(B)}{n(S)}$

$P(B) = \frac{5}{9}$

When three cards are drawn randomly,the possibilities are like ( odd, odd, even) , (even, odd, odd) and (odd, even, odd)

For, $odd, odd, even = \frac{5}{9} \times \frac{5}{9} \times \frac{4}{9}$

$even, odd, odd = \frac{4}{9} \times \frac{5}{9} \times \frac{5}{9}$

$odd, even, odd = \frac{5}{9} \times \frac{4}{9} \times \frac{5}{9}$

Probability of getting 2 odd and 1 even = $[\frac{5}{9} \times \frac{5}{9} \times \frac{4}{9}] \times [\frac{4}{9} \times \frac{5}{9} \times \frac{5}{9}] \times [\frac{5}{9} \times \frac{4}{9} \times \frac{5}{9}]$

The above relation can also be written as

$\text{Probability of getting 2 odd and 1 even} = 3 \times [\frac{4}{9} \times \frac{5}{9} \times \frac{5}{9}]$

$\text{Probability of getting 2 odd and 1 even} = 3 \times [\frac{100}{729}]$

$\text{Probability of getting 2 odd and 1 even} = [\frac{100}{243}]$

Therefore the probability of getting 1 even an d2 odd numbered card from a pack of 9 cards is $\frac{100}{243}$ when three cards are randomly drawn.

To Learn More ...

A bag contains cards numbered from 1 to 49. A card is drawn from the bag at random, after mixing the card thoroughly. Find the probability that the number on the drawn card is

(i)an odd number

(ii)a multiple of 5

(iii)a perfect square

(iv)an even prime number

https://brainly.in/question/7573143