Terrence writes down one of the numbers from 0-20 on one index card ea

Question

Terrence writes down one of the numbers from 0-20, inclusive, on one index card each until he has written each number exactly once and then faces all the cards down. Next, he randomly chooses two cards without turning them over. What is the probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number?

(A) 1/35

(B) 4/95

(C) 4/105

(D) 8/95

(E) 8/105

(A) 1/35

(B) 4/95

(C) 4/105

(D) 8/95

(E) 8/105

pushpitkc · Answer

The total ways of picking up 2 numbers from 21 numbers are  21c2 = \frac{21*20}{2}= 210

Since we have been asked to find out the probability of finding 2 prime numbers 
whose difference is a prime number, there are 8 such possibilities
For the number pairs {(2,5),(3,5),(2,7),(5,7),(2,13),(11,13),(2,19),(17,19)}

The probability that a prime number will be written on each card and that 
the absolute difference between the two prime numbers will also be a prime number is  \frac{8}{210}  =  \frac{4}{105}  (Option C)

Anannt · Answer

Ans :C

21C2=210 
And possibilities are 8 (3,5)(5,2)(5,7)(7,2)(11,13)(13,2)(17,19)(19,2)
8/210=4/105

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Luckisnoexcuse · Answer

Total number of cards are 21
21C2 Card choice
Denominator will be (21*20)/2 = 210 Option D and B are out

Prime number 2, 3, 5, 7, 11, 13, 17, 19
Difference of prime numbers be prime (Favorable selection) = (2,5) (2,7), (2,13), (2,19), (3,5), (5,7), (11,13), (17, 19) and also their reversed order i.e. (5,2) (7,2).....

(8*2)/210

8/105

Option E

TimeTraveller · Answer

Prime numbers from 0 to 20 = 2, 3, 5, 7, 11, 13, 17, 19 = 8 values.

Let  a  be the first card and  b  be the second card chosen.

Probability that each card has a prime number written on its face =  \frac{8}{21} * \frac{7}{20} = \frac{2}{3} * \frac{1}{5} = \frac{2}{15} .

Let  (a,b)  be a pair such that  |a-b|  is a prime number, such pairs are  (2,5), (2,7), (2,13), (2,19), (3,5), (5,7), (11,13), (17,19) .

No. of ways 2 cards can be chosen from 8 =  8c2 = 28 .

Probability that  |a-b|  is a prime number =  8/28 = 2/7 .

Required probability =  \frac{2}{15} * \frac{2}{7} = \frac{4}{105} . Ans - C.

Dkingdom · Answer

Hi mynamegoeson,
Since absolute difference between primes is required, does it matter whether the guy picks up in the sequence of 11-13 or 13-11?

Luckisnoexcuse · Answer

Yes i think it should be 4/105 since difference is required

Kinshook · Answer

Terrence writes down one of the numbers from 0-20, inclusive, on one index card each until he has written each number exactly once and then faces all the cards down. Next, he randomly chooses two cards without turning them over.

What is the probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number?

2 is the only even prime number. All other prime numbers are odd.
One prime number is 2(even), the other prime number is odd since difference odd(prime) and even(prime) is odd(prime)

Case 1: One prime number is 2 and other is odd such that difference is odd prime number
All such odd prime number pairs between 0-20 = {(2,5), (2,7), (2,13), (2,19)}
Favorable ways = 4C1 = 4

Case 2: Diffence between 2 odd prime numbers is 2(even prime).
All such odd prime numbers pairs = {(3,5),(5,7),(11,13),(17,19)}
Favorable ways = 4C1 = 4

Total favorable ways = 8
Total ways = 21C2 = 210

The probability that a prime number will be written on each card and that the absolute difference between the two prime numbers will itself be a prime number = 8/210 = 4/105

IMO C

Ilanchezhiyan · Answer

Help me with my approach; 
probability of picking two cards = 2/21
probability that any two of the five sets is choosen (2,5)(3,5)(7,5)(19,17)(13,11) = 2/5
Desired probability is = 2/21 * 2/5 = 4/105; 
Is this approach correct?

Terrence writes down one of the numbers from 0-20 on one index card ea

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Terrence writes down one of the numbers from 0-20 on one index card ea

Prep Toolkit

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