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A bag contains cards numbers from 1 to 49. A card is drawn from the bag at random after mixing the cards thoroughly. Find the probability that the number on the drawn card is:$( 1)$ An odd number
$( 2)$ A multiple of 5
$( 3)$ A perfect Square
$( 4)$ An even prime number.
Given: A bag containing cards numbered from 1 to 49.
To do: To find the probability of getting the drawn card to be :
(1) An odd number
(2) A multiple of 5
(3) A perfect Square
(4) An even prime number.
Solution:
Total number of cards $= 49$
$( 1)$. Total number of outcomes $=49$
The odd numbers form 1 to 49 are $1,\ 3,\ 5,\ 7,\ 9,\ 11,\ 13,\ 15,\ 17,\ 19,$ $21,\ 23,\ 25,\ 27,\ 29,$
$31,\ 33,\ 35,\ 37,\ 39,\ 41,\ 43,\ 45,\ \ 47\ and\ 49$
Total number of favourable outcomes$=25$
The probability of getting the drawn card to be an odd number
$=\frac{Total\ number\ of\ favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
$=\frac{25}{49}$
$( 2)$. Numbers multiple of 5 between $1\ to\ 49.\ are\ 5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35,\ 40,\ 45$
Here total favorable outcomes$=9$
Number of total possible outcomes$=49$
The probability of getting the drawn card to be the multiple of 5,
$=\frac{Total\ number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
$=\frac{9}{49}$
$( 3)$.The perfect squares between 1 to 49 are $1,\ 4,\ 9,\ 16,\ 25,\ 36,\ 49$
Total number of favorable outcomes$=7$
Total number of possible outcomes$=49$
The probability of getting the perfect square$=\frac{Total\ number\ of\ favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
$=\frac{7}{49}$
$=\frac{1}{7}$
$( 4)$ .We know the only even prime number is 2.
Total possible outcome$=49$
The probability of getting an even prime number $=\frac{Total\ number\ of\ favorable\ outcomes}{Total\ number\ of\ possible\ outcomes}$
$=\frac{1}{49}$
Updated on: 10-Oct-2022
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