Question

A bag contains cards numbered from 1 to 100. A card is drawn at random from the bag. Find the probability that the card drawn is (a) a multiple of 5 (b) a prime number less than 50 (c) a number greater than or equal to 80 (d) an even number

Answer 1

Step-by-step explanation:

Given total outcomes = 100

a) p(E) = no of outcomes / total outcomes

P(multiple by 5 is 5,10,15,20,25,30,35,40,45,50,55, 60,65,70,75,80,85,90,95,100) = 20/100= 1/5 or 0.2

b) p( prime no less than 50 is 2,3,5,7,11,13,17,19,23,29,31,37,39,41,43,47)= 16/100

4/25= 0.08

c) p(greater than or equal to 80 is 80.81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100)= 21/100 or 0.21

d p(even no is 100/2 = 50) 50/100= 1/2 or 0.5

Answer 2

Answer:

(a) $\frac{1}{5}$

(b) $\frac{3}{20}$

(c) $\frac{21}{100}$

(d) $\frac{1}{2}$

Step-by-step explanation:

Given that , a bag contains cards numbered from 1 to 100. A card is drawn at random from the bag.

to find the probability, (a) a multiple of 5.

(b) a prime number less than 50.

(c) a number greater than or equal to 80.

(d) an even number.

So,

By using the formula of probability ,

Probability = $\frac{favourable~~outcomes}{total ~~outcomes}$

(a) a multiple of 5 from 1 to 100 = 20.

     favourable outcomes = 20

Then, Probability = $\frac{20}{100}$

                            =$\frac{1}{5}$

(b) a prime number less than 50 = 15

( 2,3,5,7,11,13,17,19,23,29,31,27,41,43,47)

favourable outcomes = 15

Then , Probability = $\frac{15}{100}$

                             =$\frac{3}{20}$

(c) a number greater than or equal to 80.

 favourable outcomes = 21  ( from 80 to 100 )

Then , Probability = $\frac{21}{100}$

(d) an even number.

favourable outcomes = 50 ( total even number from 1 to 100 is 50 )

Then , Probability = $\frac{50}{100}$

                             = $\frac{1}{2}$

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