72% working women use computers choose 5 at random
whats the probility at least 1 does not use a computer
whats the probility that all 5 use a computer
How did you get .75 for part B?
@patrick , Kaur made a mistake. It's supposed to be (0.72)^5 which equals 0.193.
Well, isn't it interesting how no one ever asks the computers if they want to be used? Poor computers, no one ever thinks about their feelings. But let's get back to the question at hand!
To find the probability that at least one out of five randomly chosen working women does not use a computer, we need to find the probability that none of them use a computer and subtract it from 1.
Given that 72% of working women use computers, the probability that one randomly chosen working woman does not use a computer is 1 - 0.72 = 0.28. Since the events are independent, we can raise this probability to the power of 5 to find the probability that none of the five randomly chosen women use a computer. Thus, the probability is 0.28^5 ≈ 0.00547.
Now, let's find the probability that all five randomly chosen working women use a computer. Since this is the opposite event of at least one not using a computer, we can simply subtract the probability we calculated earlier from 1. Therefore, the probability that all five women use a computer is 1 - 0.00547 ≈ 0.99453.
So, the probability that at least one working woman does not use a computer is approximately 0.00547, and the probability that all five women use a computer is approximately 0.99453.
To find the probability that at least 1 out of the 5 chosen working women does not use a computer, we need to find the complement of the event where all 5 use a computer.
Step 1: Finding the probability that all 5 use a computer
The probability that an individual working woman uses a computer is given as 72%. Therefore, the probability that a randomly chosen working woman uses a computer is 0.72.
Since we want to find the probability that all 5 chosen women use a computer, we multiply the probabilities together:
P(all 5 use a computer) = (0.72)^5
Step 2: Finding the complement probability
The complement of an event is the probability of the event not happening. In this case, the complement of all 5 using a computer is at least 1 not using a computer.
Therefore, we can find the probability that at least 1 does not use a computer by subtracting the probability of all 5 using a computer from 1:
P(at least 1 does not use a computer) = 1 - P(all 5 use a computer)
Now, let's calculate these probabilities:
P(all 5 use a computer) = (0.72)^5 = 0.1681
P(at least 1 does not use a computer) = 1 - P(all 5 use a computer)
= 1 - 0.1681
≈ 0.8319
So, the probability that at least 1 out of the 5 randomly chosen working women does not use a computer is approximately 0.8319 or 83.19%.
The probability that all 5 of the randomly chosen working women use a computer is approximately 0.1681 or 16.81%.
a) the probability that at least 1 doesnt use a computer at work
Because the question asks for at least 1 that doesn't we have to do the opposite complement.
P(E)=1-P(complement)
Probablity of not using computer(NUC)=1 - Probability of using computer P(NUC)= 1-P(UC)
P(UC)= 0.72
P(using computer 5 times)=(0.72)(0.72)(0.72)(0.72)(0.72) or (0.72)^5=0.19349
P(NUC)= 1-(0.72)^5= 0.807
b) The probability that all 5 use a computer in their jobs
P(C)=P(C*C*C*C*C)=(0.75)(0.75)(0.75)(0.75)(0.75)=(0.75)^5=.194