91Ó°ÊÓ

Each of the following statements demonstrate a common misuse of probability. Explain what is wrong with each statement: (a) Approximately \(10 \%\) of adults are left-handed. So, if we take a simple random sample of 10 adults, 1 of them will be left-handed. (b) A pitch in baseball can be called a ball or a strike or can be hit by the batter. As there are three possible outcomes, the probability of each is \(1 / 3\). (c) The probability that a die lands with a 1 face up is \(1 / 6 .\) So, since rolls of the die are independent, the probability that two consecutive rolls land with a 1 face up is \(1 / 6+1 / 6=1 / 3\). (d) The probability of surviving a heart attack is \(2.35 .\)

Step by step solution

01

Misuse A

The first statement is incorrect because probability doesn't guarantee exact outcomes. Although \(10 \%\) of adults being left-handed does increase chances for at least one to be left-handed in a group of 10, it doesn't ensure one will be left-handed in every group of 10 adults sampled.

02

Misuse B

The second statement incorrectly assumes that the three listed outcomes are equally likely. However, in a game of baseball, multiple factors contribute to whether a pitch is a ball, a strike, or hit by the batter, which likely result in varying probabilities for each of these outcomes.

03

Misuse C

The third statement incorrectly adds the probabilities of two independent events. The correct way to find the probability of two independent events both occurring is to multiply the probability of each individual event. Therefore, the correct probability of rolling a 1 twice in a row is \(\frac{1}{6} * \frac{1}{6} = \frac{1}{36}\).

04

Misuse D

The fourth statement is incorrect because probability values range from 0 (event will definitely not happen) to 1 (event will definitely happen). A probability greater than 1 (such as 2.35) doesn't make sense, which suggests this value is misunderstood or misrepresented.

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