A study found that 81% of households
in the United States have computers. Of those 81%, 92% have Internet
access. Find the probability that a U.S. household selected at random has a
computer and has Internet access.
0.745
P(A and B) = P(A) * P(B/A)
= (0.81)* (0.92)
= 0.745
The probability that a U.S. household selected at random has a
computer and has Internet access is 0.745
Well, if 81% of households in the United States have computers and 92% of those households with computers have Internet access, that means that only 75% of U.S. households have both a computer and Internet access.
So, the probability that a U.S. household selected at random has a computer and has Internet access is 75%. That's pretty high, but it's still not as high as the probability of me finding a matching pair of socks in my drawer.
To find the probability that a U.S. household selected at random has a computer and has Internet access, we need to find the joint probability.
Step 1: Calculate the probability of a U.S. household having a computer.
Given that 81% of households have computers, the probability of a U.S. household having a computer is 0.81 or 81/100.
Step 2: Calculate the probability of a U.S. household with a computer having Internet access.
Given that 92% of households with computers have Internet access, the probability of a U.S. household with a computer having Internet access is 0.92 or 92/100.
Step 3: Calculate the joint probability.
The joint probability is the product of the probabilities from steps 1 and 2.
Probability = (probability of having a computer) x (probability of having Internet access)
= (81/100) x (92/100)
= 0.81 x 0.92
= 0.7452
Therefore, the probability that a U.S. household selected at random has a computer and has Internet access is 0.7452 or 74.52%.
To find the probability that a U.S. household selected at random has a computer and has Internet access, you can multiply the probabilities of the two events: the probability of having a computer and the probability of having Internet access given that they have a computer.
First, let's find the probability of having a computer. According to the study, 81% of U.S. households have computers. This means that the probability of a randomly selected household having a computer is 0.81 or 81%.
Next, we need to find the probability of having Internet access given that they have a computer. The study states that 92% of households with computers have Internet access. This means that the probability of having Internet access given that they have a computer is 0.92 or 92%.
To find the overall probability, we multiply these two probabilities together:
Probability = Probability of having a computer * Probability of having Internet access given a computer
Probability = 0.81 * 0.92
Calculating this:
Probability = 0.7452
Therefore, the probability that a U.S. household selected at random has a computer and has Internet access is approximately 0.7452 or 74.52%.