If an integer is to be randomly selected from set M above

Question

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

Bunuel · Accepted Answer

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.

kbulse · Answer

I think D is correct
in order to get negative integer either m should be negative and n positive
probability of m is negative =5/5=1
probability of n is positive 3/6=1/2
probability of m negative and m positive is 1*1/2=1/2

x2suresh · Answer

P= No of ways the product of two integers is negative/All possible values 
 = 5*3/5*6 =1/2

srivas · Answer

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

jeeteshsingh · Answer

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

Probability = 15 / 30 = 1/2

bangalorian2000 · Answer

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

JeffTargetTestPrep · Answer

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

LeoN88 · Answer

total combinations-> 5C1 * 6C1
Combinations that gives us -ve value upon multiplication-> 5C1 * 3C1.

15/30, probability is 1/2.  D

m7runner · Answer

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.

Komal324 · Answer

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 · Answer

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.

GmatKnightTutor · Answer

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.

Manbhav7 · Answer

For Product to be a negative number, we need 1 -ve number and 1 +ve number -

From M - We can choose all integers thus, 6 ways --- (1)
From T, We can only choose 3 integers (1,2,3 not Zero or any other -ve), thus 3 ways ----(2) 
Total Ways of choosing - 6x6 = 36

Therefore- (1) x (2)/ Total ways = 6x3/36 = 1/2

Bunuel  - Can you tell me if this approach will work as well? Thanks

Bunuel · Answer

There are 5 numbers in Set M, not 6. So the correct probability of getting a negative product is:

5/5 * 3/6 = 1/2.

If an integer is to be randomly selected from set M above

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