Question

Cards, numbered 3, 4, 5 ..., 25 are put in a box and mixed
thoroughly. A card is drawn at random from the box. Find the
probability that the card drawn bears (i) an even number (11) a
number divisible by 2 or 3.​

Answer 1

Correct Question:

Cards, numbered 1, 2, 3, 4, 5 ..., 25 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears (i) an even number (ii) a number divisible by 2 or 3.

Step-by step explanation :

i) Total number of cards = 25

P(an even number) = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 = 12

Probability = Number of favourable outcomes/Total number of outcomes

$\implies$ 12/25

ii) Total number of cards = 25

P(a number divisible by 2 or 3) = 2, 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24 = 16

Probability = Number of favourable outcomes/Total number of outcomes

$\implies$ 16/25

But if the given question is correct then,

Question :

Cards, numbered 3, 4, 5 ..., 25 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears (i) an even number (ii) a number divisible by 2 or 3.

Step-by-step explanation :

i) Total number of cards = 23

P(an even number) = 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 = 11

Probability = Number of favourable outcomes/Total number of outcomes

$\implies$ 11/23

ii) Total number of cards = 23

P(a number divisible by 2 or 3) = 3, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24 = 15

Probability = Number of favourable outcomes/Total number of outcomes

$\implies$ 15/23

Answer 2

Question :--- Cards, numbered 3, 4, 5 ..., 25 are put in a box and mixed thoroughly. A card is drawn at random from the box. Find the probability that the card drawn bears (i) an even number (ii) a number divisible by 2 or 3. ?

Concept used :---

→ Probability :-- The number of ways of achieving success / the total number of possible outcomes.

_____________________________

Solution :----

it is Given that , Numbers are from 3 to 25 continuously .

So,

→ Total Number of Possible Outcomes = 25 - 2(First number and second Number ) = 23 Total.

___________________________

Answer (1) :---

→ Total Even Numbers From 3 to 25 .

First Lets See what is a even Number ?

→ Even Number :-- Any integer that can be divided exactly by 2 is an even number.

So,

→ Even Numbers from 3 to 25 are = 4, 6, 8 , 10 , 12 , 14 , 16 , 18 , 20, 22 , and 24 = 11 Total .

So,

→ Required Probability of selecting a even Number out of total number will be = 11/23 ..

_____________________________

Answer (2) :----

it has been said that a number either divisible by 2 or 3.

As told above all even Numbers are Multiple of 2 , So clearly we have Those 11 numbers...

And, Multiple of 3, upto 25 that are not Divisible by 2 are left as = 3, 9, 15 and 21 = 4 Total .

So, Total Number That will be divisible by 2 or 3 are = 11 + 4 = 15 Total .

Hence,

→ Required Probability = 15/23. (Ans).