James has 10 shirts in his drawer: 3 red, 2 black and 5 white. He has 6 pairs of shorts in his drawer: 3 black, 1 blue, and 2 khaki. What is the probability that a shirt and a pair of shorts chosen at random are both black? ______________________
2/10 * 3/6 = ____
1/10
Well, if James has 10 shirts and 6 pairs of shorts in his drawer, that means he has a lot of options. But we're only interested in the black ones, right? So, out of the 10 shirts, 2 are black, and out of the 6 pairs of shorts, 3 are black.
To find the probability of getting a black shirt and a black pair of shorts, we just multiply the probabilities of selecting each individually.
So, the probability of selecting a black shirt is 2/10, and the probability of selecting a black pair of shorts is 3/6.
Multiply those together, and you get (2/10) * (3/6) = 6/60.
Now, find the simplest form of that fraction, and you get 1/10.
So, the probability that a shirt and a pair of shorts chosen at random are both black is 1/10.
And now you know why James always rocks that black outfit!
To find the probability that a shirt and a pair of shorts chosen at random are both black, we need to determine the total number of possible outcomes and the number of favorable outcomes.
Let's first calculate the total number of possible outcomes. James has a total of 10 shirts and 6 pairs of shorts, so there are 10 * 6 = 60 possible outcomes.
Next, let's calculate the number of favorable outcomes. James has 2 black shirts and 3 black pairs of shorts, so there are 2 * 3 = 6 favorable outcomes.
Finally, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Favorable outcomes / Total outcomes
Probability = 6 / 60
Probability = 1/10
Therefore, the probability that a shirt and a pair of shorts chosen at random are both black is 1/10.
To find the probability that a shirt and a pair of shorts chosen at random are both black, we need to find the probability of selecting a black shirt and a pair of black shorts.
First, let's find the probability of selecting a black shirt.
James has a total of 10 shirts, out of which 2 are black. Therefore, the probability of selecting a black shirt is 2/10, or 1/5.
Next, let's find the probability of selecting a pair of black shorts.
James has a total of 6 pairs of shorts, out of which 3 are black. Therefore, the probability of selecting a pair of black shorts is 3/6, or 1/2.
Finally, to find the probability that both events occur (i.e., selecting a black shirt and a pair of black shorts), we calculate the product of the individual probabilities:
(1/5) * (1/2) = 1/10
Therefore, the probability that a shirt and a pair of shorts chosen at random are both black is 1/10.