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marcodonzelli
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?

A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5

P= No of ways the product of two integers is negative/All possible values
= 5*3/5*6 =1/2
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M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?

A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5

Soln: Total number of possible ways of choosing two integers is = 5 * 6 = 30 ways
Now for the product of two integers to be chosen to be negative = they should be of opposite sign. Since set M has all negative numbers, thus we move to set T which has 3 positive numbers.
Thus total number of possible ways in which product will be negative is = 5 * 3 = 15

Probability that the product of the two integers will be negative
= 15/30
= 1/2
Ans is D
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marcodonzelli
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?

A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5

Negative prod pairs = 5 x 3 = 15
total pairs possible = 5c1 x 6c1 = 5 x 6 = 30

Probability = 15 / 30 = 1/2
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If product has to be negative then m is -ve and n is +ve or m is +ve and n is -ve. But all elements of m are -ve hence we need n to be +ve.
0 has to be excluded as any number multiplied by 0 is 0 and it is neither +ve nor -ve.

p(m&n) = p(m)*p(n) = 1*3/6 = 1/2 hence D
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marcodonzelli
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?

A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5

In order for the product of the two integers to be negative, one of them has to be negative and the other has to be positive. Since every integer in set M is negative, we must select a positive integer in set T.
Thus, the probability of selecting a negative number in set M and then a positive number in set T is:

5/5 x 3/6 = 1/2

Answer: D
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marcodonzelli
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?

A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5

total combinations-> 5C1 * 6C1
Combinations that gives us -ve value upon multiplication-> 5C1 * 3C1. [5C1 for M and 3C1 for T]

15/30, probability is 1/2. D
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marcodonzelli
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?

A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5

The product of two integers will be negative (lets call this, say [K]) when the signs are opposite for both integers.
Since set M contains negative integers, the probability of K occurring (P(K)) hinges on set T which has 3 positive integers out a total of 6 integers.

Hence P(K) = \(\frac{3}{6}\) = \(\frac{1}{2}\)

Answer choice (D) is correct, IMO.
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Dear Bunuel,

Hope you are doing well. I got the right answer to the question. However, I have one doubt- did we assume that we will follow the order to first pick the numbers from M and then from T? Cannot it be the other way around? Shouldn't we consider both the cases no matter that the cases will be repetitive?

In other words, I am trying to say that 5*3=15 is the favourable outcome (we first pick from M and then from T). Then, again 5*3=15 is the favourable outcome (we first pick from T and then from M). So, total favourable outcome is 15+15=30.

Hope my query is clear.
Thank you for your support.

Best,
Komal

Bunuel
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?


A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5

In order the product of two multiples to be negative they must have different signs. Since Set M consists of only negative numbers then in order mt to be negative we should select positive number from set T, the probability of that event is 3/6=1/2, (since out of 6 number in the set 3 are positive).

Answer: D.

Hope it's clear.
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Komal324
Dear Bunuel,

Hope you are doing well. I got the right answer to the question. However, I have one doubt- did we assume that we will follow the order to first pick the numbers from M and then from T? Cannot it be the other way around? Shouldn't we consider both the cases no matter that the cases will be repetitive?

In other words, I am trying to say that 5*3=15 is the favourable outcome (we first pick from M and then from T). Then, again 5*3=15 is the favourable outcome (we first pick from T and then from M). So, total favourable outcome is 15+15=30.

Hope my query is clear.
Thank you for your support.

Best,
Komal

Bunuel
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?


A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5

In order the product of two multiples to be negative they must have different signs. Since Set M consists of only negative numbers then in order mt to be negative we should select positive number from set T, the probability of that event is 3/6=1/2, (since out of 6 number in the set 3 are positive).

Answer: D.

Hope it's clear.

Order doesn’t matter here. Picking from M then T or T then M gives the same product, so we don’t count it twice.
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marcodonzelli
M = {-6, -5, -4, -3, -2}
T = {-2, -1, 0, 1, 2, 3}

If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative?

A. 0
B. 1/3
C. 2/5
D. 1/2
E. 3/5
For the product of two integers to be negative, they have to have opposing signs (i.e. +ve integer multiplied by a -ve integer OR -ve integer multipled by +ve integer).

All 5 integers from SET M, integers which are each negative, can therefore work with the 3 positive integers in Set T (1, 2, 3) to create a negative result.

5 multipled by 3 = 15

Since we're looking for a probability, we need to know the total number of products that can be created. Each of the 5 integers in Set M can be multiplied with each of the 6 integers in Set T.

5 multipled by 6 = 30

The probability is therefore:

15/30 = 1/2

(D) is your answer.
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