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Q.

A box contains 20 cards numbered from 1 to 20.  A card is drawn at random from the box. Find the probability that the number on the drawn card is a prime number.


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a

3 5  

b

1 5  

c

2 5  

d

3 7   

answer is C.

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Detailed Solution

As the box contains 20 cards numbered from 1 to 20.  A card is drawn at random from the box. So,
The formula of the probability of an event is the number of favorable outcomes divided by the total number of outcomes.
P(E)= no. of favorable outcomes  total number of outcomes  
Let E   be event of drawing a card with prime number from the cards with numbered from 1 to 20.
Prime numbers from 1 to 20 are  2,3,5,7,11,13,17,19   No. of favorable outcomes is 8
Total number of possible outcomes is 20
The probability that the number on the drawn card is prime number is
P(E) = no. of favorable outcomes   total number of outcomes  P(E) = 8 20 P(E) = 2 5  
Therefore, probability that a card with prime number is selected from 1 to 20 is 2 5   .
Hence, option 3 is correct.
 
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