Probability

priyankamishra11 wrote: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

Can anyone please explain how to solve ths question.?

integer M * integer T = negative

We dont have to worry about selecting from M because all the integers are negative.

Set T = 3 positive integers [1,2,3] remember 0 is not positive.

probability of choosing positive integer from set T = 3/6 = 1/2.

Thus, 1/2 is the answer.

OA?

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


Total product possibilities is 30 (5 set m * 6 set T)

Any number multiplied by 0 is 0 which is neither positive nor negative.

Every number in set M has 3 possibilities to be paired with set T numbers and the product truning out to be negative.
There are 5 numbers so 5*3 =15 such possibilities

P = no of fav outcomes/total possible outcomes

= 15/30 = 1/2

First set we can ignore as all numbers are negative
for result to be negative second no has to be positive
we have 3 such nos out of 12
ie 3 / 6 = 1 / 2

Probability of an event occurring=number of favourable outcomes/number of all possible outcomes
hence,
number of favourable outcomes=5p1x3p1
number of all possible outcomes=5p1x6p1
therefor, 5p1x3p1/5p1x6p1=15/30=1/2

Note: we can only pick negative number from the set M and positive numbers from the set T then only the product would be Negative.

Thanks,
Surbhi

possible/total

5*3/5*6=1/2

priyankamishra11 wrote: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

Can anyone please explain how to solve ths question.?

2 approaches are possible

approach 1) probability method, P(selecting negative from set M)=1, P(selecting positive from set T)=3/6. P(negative as product)=1*3/6=1/2

approach 2) counting method, selecting one negative out of 5 negatives 5C1=5 ways, selecting one positive out of 3 positives 3C1=3, total number of outcomes 5*6=30. P(negative as product)=#favorable outcomes/#total outcomes=5*3/30=1/2