Question

In a survey of consumers aged 12 and​ older, respondents were asked how many cell phones were in use by the household.​ (No two respondents were from the same​ household.) Among the​ respondents, answered​ "none," said​ "one," said​ "two," said​ "three," and responded with four or more. A survey respondent is selected at random. Find the probability that​ his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in​ use? Consider an event to be unlikely if its probability is less than or equal to 0.05.

Answer 1

The probability that​ his/her household has four or more cell phones in use is 0.122 or 12.2%.

Explanation:

The complete question is: In a survey of consumers aged 12 and​ older, respondents were asked how many cell phones were in use by the household.​ (No two respondents were from the same​ household.) Among the​ respondents, 215 answered​ "none", 280 said​ "one", 362 said​ "two", 149 said​ "three," and 140 responded with four or more. A survey respondent is selected at random. Find the probability that​ his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in​ use? Consider an event to be unlikely if its probability is less than or equal to 0.05.

We are given that among the​ respondents, 215 answered​ "none", 280 said​ "one", 362 said​ "two", 149 said​ "three," and 140 responded with four or more.

A survey respondent is selected at random.

As we know that the probability of any event is calculated as;

Probability =
`\frac{\text{Favorable number of outcomes}}{\text{Total number of outcomes}}`

Here, we have to find the probability that​ his/her household has four or more cell phones in use;

Number of respondent having four or more cell phones in use = 140

Total number of respondents asked = 215 + 280 + 362 + 149 + 140 = 1146

So, the required probability =
`(140)/(1146)`

= 0.122 or 12.2%

No, it is not unlikely for a household to have four or more cell phones in​ use because the probability is not less than or equal to 0.05 but in actual it is greater than 0.05.