(i )A bag containing cards numbered 1 to 49. Find the probability that the number on the drawn card is : an odd number

(ii) A bag containing cards numbered 1 to 49. Find the probability that the number on the drawn card is : a multiple of 5

(iii) A bag containing cards numbered 1 to 49. Find the probability that the number on the drawn card is : even prime

(i) It is given that a bag contains cards numbered 1 to 49 and we need to find the probability that the number on the drawn card is an odd number.

Sample Space, 𝑆 = {1, 2, 3, ..., 49}

Therefore, number of possible outcomes = 49

Now, the odd numbers are {1, 3, 5, 7, 9, ..., 49} = 25

Therefore, number of favourable outcomes = 25

It is known that the probability of an event is given by the ratio of the number of favourable outcomes to the number of possible outcomes. Mathematically,

$P\left(E\right) = \frac{number of favourable outcomes }{total number of outcomes}$

Where 𝐸 is any event and 𝑃(𝐸) is the probability of the event 𝐸.

Therefore, the probability of the event that odd number is drawn is calculated as

$P(odd number) = \frac{25}{49}$

Hence, the probability that the selected number is odd is = $\frac{25}{49}$

(ii) It is given that a bag contains cards numbered 1 to 49 and we need to find the probability that the number on the drawn card is a multiple of 5.

Sample Space, 𝑆 = {1, 2, 3, ..., 49}

Therefore, number of possible outcomes = 49

Now, multiples of 5 are {5, 10, 15, 20, 25, 30, 35, 40, 45} = 9

Therefore, number of favourable outcomes = 9

It is known that the probability of an event is given by the ratio of the number of favourable outcomes to the number of possible outcomes. Mathematically,

$P\left(E\right) = \frac{number of favourable outcomes }{total number of outcomes}$

$P(multiple of 5) = \frac{9}{49}$

(iii) It is given that a bag contains cards numbered 1 to 49 and we need to find the probability that the number on the drawn card is even prime.

Sample Space, 𝑆 = {1, 2, 3, ..., 49} Therefore, number of possible outcomes = 49 Now, the even primes are {2} = 1

Therefore, number of favourable outcomes = 1

It is known that the probability of an event is given by the ratio of the number of favourable outcomes to the number of possible outcomes. Mathematically,

$P\left(E\right) = \frac{number of favourable outcomes }{total number of outcomes}$

$P(even prime) = \frac{1}{49}$

Hence, the probability that the selected number is odd is $\frac{1}{49}$