A box contains 150 black pens and 50 red pens. Jose said the sum of the probability that a randomly selected pen will not be black and the probability that the pen will not be red is 1. Explain whether you agree.
THANK YOU!!
prob(red pen) = 50/200 = 1/4
prob(not red) = 3/4
prob(black pen) = 150/200) = 3/4
prob(not black) = 1/4
their sum = 3/4 + 1/4 = 1
answer
1/4
The answer is yes because the probability of the red pen is 25 percent(1/4). The percentage of the not red is 75 percent(3/4). The probability of the black pen is 75 percent(3/4). The probability of the not black is 25 percent(1/4). If you add these together you get 1, which is what Jose said. Therefore, the answer is yes.
To determine whether you agree with Jose's statement, you need to calculate the probability that a randomly selected pen is not black and the probability that it is not red, and then add those two probabilities together.
First, let's calculate the probability that a randomly selected pen is not black. The total number of pens in the box is 150 + 50 = 200. Since there are 150 black pens, the probability of selecting a pen that is not black is given by:
Probability(not black) = 1 - Probability(black)
= 1 - (number of black pens / total number of pens)
= 1 - (150 / 200)
= 1 - 0.75
= 0.25
Next, let's calculate the probability that a randomly selected pen is not red. The total number of pens is still 200, but this time we have 50 red pens. So the probability of selecting a pen that is not red is:
Probability(not red) = 1 - Probability(red)
= 1 - (number of red pens / total number of pens)
= 1 - (50 / 200)
= 1 - 0.25
= 0.75
Now, let's add these two probabilities together:
Probability(not black) + Probability(not red) = 0.25 + 0.75 = 1
As you can see, the sum of the probability that a randomly selected pen will not be black and the probability that it will not be red is indeed 1. Therefore, you agree with Jose's statement.