Related questions with answers

The data in the following table show the outcomes of guilty and not-guilty pleas in $1028$ criminal court cases.

	Guilty Plea	Not-Guilty Plea
Sent to prison	$392$	$58$
Not sent to prison	4564$	$14$

Source: Brereton and Casper, Law and Sodety Revicw, Vol. $16$ , No. $7$ .

a. What is the probability that a randomly selected defendant either pled guilty or was sent to prison?

b. What is the probability that a randomly selected defendant either pled not guilty or was not sent to prison?

Use the table to answer the following questions.

Year	U.S. Population (millions)	Traffic Fatalities	Licensed Drivers (millions)	VehicleMiles (trillions)
$1995$	$263$	$41,817$	$177$	$2.4$
$2000$	$282$	$41,945$	$190$	$2.7$
$2005$	$296$	$43,510$	$201$	$3.0$
$2010$	$309$	$32,885$	$210$	$3.0$

Express the $2010$ fatality rate in deaths per $100,000$ licensed drivers.

Suppose you study family income in a random sample of $300$ families. You find that the mean family income is $\$ 55,000$ ; the median is $\$ 45,000$ ; and the highest and lowest incomes are $\$ 250,000$ and $\$ 2400$ , respectively.

a. Draw a rough sketch of the income distribution, with clearly labeled axes. Describe the distribution as symmetric, left-skewed, or right-skewed.

b. How many families in the sample earned less than $\$ 45,000$ ? Explain how you know.

c. Based on the given information, can you determine how many families earned more than $\$ 55,000$ ? Why or why not?

Question

Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

I haven't won in my last $25$ pulls on the slot machine, so I must be having a bad day and I'm sure to lose if l play again.

Solution

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The probability of winning in each pull on the slot machine is constant. Hence, losing in the past $25$ pulls will not affect the chance of winning in the next pull.

Thus, the given statement does not make sense.

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Related questions with answers

Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning. I haven't won in my last 252525 pulls on the slot machine, so I must be having a bad day and I'm sure to lose if l play again.

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More related questions

Decide whether each of the following statements makes sense (or is clearly true) or does not make sense (or is clearly false). Explain your reasoning.

I haven't won in my last $25$ pulls on the slot machine, so I must be having a bad day and I'm sure to lose if l play again.