Final answer:
To find the probability that six randomly selected Americans all had the same influenza status, we multiply the probability of having the virus by itself six times and add it to the probability of not having the virus multiplied by itself six times. The answer is (a) 0.1184.
Step-by-step explanation:
To find the probability that six randomly selected Americans all had the same influenza status, we need to multiply the probability of having the influenza virus by the probability of not having the influenza virus. According to the CDC, the probability of contracting the influenza virus is 30%. So the probability of having the virus is 0.30 and the probability of not having the virus is 0.70 (1 - 0.30).
To find the probability that all six Americans have the same influenza status, we need to multiply the probability of having the virus by itself six times, or multiply the probability of not having the virus by itself six times. Since we don't know the vaccination status of the individuals, we need to consider both possibilities.
If all six Americans have the influenza virus, the probability would be 0.30^6 = 0.000729. If all six Americans do not have the influenza virus, the probability would be 0.70^6 = 0.117649.
Since we are looking for the probability that six randomly selected Americans all had the same influenza status (either all having the virus or all not having the virus), we need to add the probabilities of both scenarios. So the final probability is 0.000729 + 0.117649 = 0.118378, which is approximately equal to 0.1184.
Therefore, the answer is (a) 0.1184.