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If p and q are two distinct numbers chosen from the set ..............

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If p and q are two distinct numbers chosen from the set ..............  [#permalink]

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New post 30 Jan 2019, 01:43
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A
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E

Difficulty:

  55% (hard)

Question Stats:

44% (01:37) correct 56% (02:42) wrong based on 42 sessions

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If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.

    A. \(\frac{1}{30}\)

    B. \(\frac{1}{15}\)

    C. \(\frac{1}{9}\)

    D. \(\frac{2}{15}\)

    E. \(\frac{2}{9}\)


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Re: If p and q are two distinct numbers chosen from the set ..............  [#permalink]

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New post 30 Jan 2019, 02:07
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prime factors in the set: -3, -2, 2, 3, 5
Each product with 1 or -1 is also prime.
5*2/10C2=10/45=2/9→(E)

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If p and q are two distinct numbers chosen from the set ..............  [#permalink]

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New post Updated on: 01 Feb 2019, 09:21
prime no are +ve integer value (2,3,5)
2,3,5 can be formed ( -3,-1) ,( -2,-1), ( 1,2), ( 1,3),(1,5) ; total 5 pairs p*q can be 2 ways; 5*2 = 10

total pairs = 5 and p*q = 10c2
5/10c2 ; 5/45
=1/9
IMOC

EgmatQuantExpert wrote:
If p and q are two distinct numbers chosen from the set {-4,-3, -2, -1, 0, 1, 2, 3, 4, 5}. Find the probability that p * q is a prime number.

    A. \(\frac{1}{30}\)

    B. \(\frac{1}{15}\)

    C. \(\frac{1}{9}\)

    D. \(\frac{2}{15}\)

    E. \(\frac{2}{9}\)


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Originally posted by Archit3110 on 30 Jan 2019, 07:04.
Last edited by Archit3110 on 01 Feb 2019, 09:21, edited 1 time in total.
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Re: If p and q are two distinct numbers chosen from the set ..............  [#permalink]

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New post 01 Feb 2019, 01:57
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Solution


Given:
    • A set of 10 integers, {-4, -3, -2, -1, 0, 1, 2, 3, 4, 5}
    • p and q are two distinct integers chosen from the given set

To find:
    • The probability that p * q is a prime number

Approach and Working:
The total number of ways of choosing two distinct integers from a set of 10 elements = \(^{10}C_2 = 45\)

Now, for p * q to be prime, one of them must be ±1 and the other must be = ± a prime number.
    • Thus, the possible cases are {-1, -2}, {-1, -3}, {1, 2}, {1, 3}, {1, 5}

Therefore, probability = \(\frac{5}{45} = \frac{1}{9}\)

Hence the correct answer is Option C.

Answer: C

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Re: If p and q are two distinct numbers chosen from the set ..............   [#permalink] 01 Feb 2019, 01:57
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