A recent poll conducted by Gallup Inc. asked the following question:

In general, how much trust and confidence to you have in the mass media - such as newspapers, TV, and radio - when it comes to reporting the news fully, accurately, and fairly? A great deal, a fair amount, not very much, or non at all?

58% of respondents has a negative view of the media, meaning they responded with either not very much or non at all.

Two people are randomly chosen, each is asked the poll question above. What is the probability?

Two people are randomly chosen, each is asked the poll question above. What is the probability

Part (a) that both have a negative view of mass media?
Part (b) neither have a negative view of the mass media?
Part (c) at least one of the two has a negative view towards the media?

C) should me 1 - b

If the events are independent, the probability of both/all events occurring is determined by multiplying the probabilities of the individual events.

(a) .58 * .58

(b) .42 * .42

(c) "at least one" = one or two

P(2) = (a)

P(1) = .58 * .42

Either-or probabilities are found by adding the individual probabilities.

hi so how exactly did you figure out C

Well, let's tackle these probabilities one by one with a touch of clownish humor!

Part (a) - What is the probability that both have a negative view of mass media?

Well, if 58% of people have a negative view, that means there is a 42% (100% - 58%) chance of having a positive view. Since the two respondents are randomly chosen and their responses are independent, we can multiply the probabilities together.

So, the probability that both have a negative view is 0.58 * 0.58 = 0.3364, or approximately 33.64%.

Part (b) - What is the probability that neither have a negative view of the mass media?

If 42% of people have a positive view, then the probability of neither having a negative view is 0.42 * 0.42 = 0.1764, or approximately 17.64%.

Part (c) - What is the probability that at least one of the two has a negative view towards the media?

The easiest way to calculate this is to find the probability that neither have a negative view (from part b) and subtract it from 1, because we want the opposite scenario.

So, the probability that at least one of the two has a negative view is 1 - 0.1764 = 0.8236, or approximately 82.36%.

Remember, these probabilities are based on the poll results given and are not reflective of the overall population. Keep that in mind when interpreting the results!

To calculate the probabilities, we need to first find the probability of a single event occurring and then apply the appropriate formulas based on the scenario described in each part.

Let's denote "N" as a negative view and "P" as a positive view of the mass media.

Given: 58% of respondents have a negative view, which means 42% have a positive view.

Part (a) - Both have a negative view of mass media:
To find the probability that both randomly chosen people have a negative view, we multiply the individual probabilities together.
P(a) = P(N) × P(N) = (0.58) × (0.58) = 0.3364 (33.64%)

Part (b) - Neither have a negative view of the mass media:
To find the probability that neither of the randomly chosen people has a negative view, we need to find the probability that both have a positive view.
P(b) = P(P) × P(P) = (0.42) × (0.42) = 0.1764 (17.64%)

Part (c) - At least one of the two has a negative view towards the media:
To find the probability that at least one of the randomly chosen people has a negative view, we need to consider the complement rule. That is, the probability of the opposite event (both having positive views) subtracted from 1.
P(c) = 1 - P(b) = 1 - 0.1764 = 0.8236 (82.36%)

Therefore:
- The probability that both randomly chosen people have a negative view is 33.64% (0.3364).
- The probability that neither of the randomly chosen people has a negative view is 17.64% (0.1764).
- The probability that at least one of the two has a negative view towards the media is 82.36% (0.8236).