Question

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

Answer 1

Hint- Here, we need to find the number of favourable outcomes and total number of outcomes for each event and then apply the formula of probability to every event and find the required probability of each case.

Complete step-by-step answer:
As given cards are marked with numbers from 1 to 49
Therefore, total number of outcomes = 49
(i) Let E1 = Event of getting an odd number
Numbers which are odd in this range =1,3,5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49
Number of outcomes favourable to E1 =25
Probability(E1)$= \dfrac{{{\text{No}}{\text{. of favourable outcomes}}}}{{{\text{Total number of outcomes}}}}$ $= \dfrac{{25}}{{49}}$
Hence, the probability of getting an odd number $= \dfrac{{25}}{{49}}$
(ii) Let E2 = Event of getting a number which is a multiple of 5
Numbers which are multiple of 5 = 5,10,15,20,25,30,35,40,45
Number of outcome favourable to E2 = 9
P(E2) $= \dfrac{9}{{49}}$
Hence, the probability required to get a multiple of 5 $= \dfrac{9}{{49}}$
(iii) Let E3 = Event of getting a number which is a perfect square
Numbers which are perfect squares = 1,4,9,16,25,36,49
Number of outcomes favourable to E3 = 7
P(E3)$= \dfrac{7}{{49}} = \dfrac{1}{7}$
Hence, the probability required to get a perfect square $= \dfrac{1}{7}$
(iv) Let E4 = Event of getting an even prime number
Numbers which are even and prime = 2
Number of outcomes favourable to E4 = 1
P(E4)$= \dfrac{1}{{49}}$
Hence, the probability required to get an even prime number $= \dfrac{1}{{49}}$.

Note- One needs to remember the formula of probability and carefully find the no. of favourable outcomes and divide them with total number of outcomes. One should carefully write the number of favourable outcomes in each case as forgetting one number can make your whole effort in vain. Remember the number of total outcomes remains the same as there are always 49 numbers in the bag.