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Q.

Cards, on which numbers 1,2,3, ..........100 are written (one number on one card and no number is repeated ) are put in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that card taken out has a number which is a multiple of 13


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a

7 100  

b

1

c

0

d

0.2 

answer is A.

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Detailed Solution

Given: -
Numbers 1,2,3, ..........100 on the card are written and put in a bag and mixed. To find the probability that  a number which is a multiple of 13.
So, the total number of outcomes is, n(S) = 100.
Let E be the event of selecting numbers that are multiple of 13.
The favourable outcomes are multiple of 13.
The multiples of 13 are 13, 26, 39, 52, 65, 78, 91.
Thus, n(E) = 7.
The probability of the random experiment is P E   given by the formula,
P E = Number of favourable outcomes n(E) Total number of possible outcomes n(S)  
⇒P(E)= 7 100  
The probability that the card is taken out has a number which is a multiple of 13 is 7 100  .
So, the correct option is 1.
 
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Cards, on which numbers 1,2,3, ..........100 are written (one number on one card and no number is repeated ) are put in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that card taken out has a number which is a multiple of 13