#12.2 Independent and Dependent Events

A box contains an assortment of tool items on clearance. You randomly choose a sale item, look at it, and then put it back in the box. Then you randomly choose another sale item.

Event A: You choose a hammer first.

Event B: You choose a pair of pliers second

Are these independent or dependent events?

• Independent

• Dependent

A cooler contains an assortment of juice boxes. You randomly choose a juice box and drink it. Then you randomly choose another juice box.

Event A: You choose an orange juice box first.

Event B: You choose a grape juice box second

Are these independent or dependent events?

• Independent

• Dependent

You are playing a game that requires rolling a die twice. Use a sample space to determine whether rolling a 2 and then a 6 are independent events.

Are the events independent?

• Yes, the events are independent.

• No, the events are not independent.

A game show host picks contestants for the next game, from an audience of 150. The host randomly chooses a thirty year old, and then randomly chooses a nineteen year old. Use a sample space to determine whether randomly choosing a thirty year old first and randomly selecting a nineteen year old second are independent events

• The events are independent.

• The events are not independent.

A hat contains 10 pieces of paper numbered from 1 to 10. You randomly choose the number 1, you replace the number, and then you randomly choose the number 10.

Find the probability of this occurring.

• $\frac{1}{10}$

• $\frac{1}{5}$

• $\frac{1}{20}$

• $\frac{1}{100}$

A hat contains 10 pieces of paper numbered from 1 to 10. You randomly choose the number 5, you do not replace the number, and then you randomly choose the number 6. 

Find the probability of this occurring.

•  $\frac{1}{11}$ 

• $\frac{1}{5}$

•  $\frac{1}{90}$ 

•  $\frac{1}{50}$ 

The probability that a stock increases in value on a Monday is 60%. When the stock increases in value on Monday, the probability that the stock increases in value on Tuesday is 80%. What is the probability that the stock increases in value on both Monday and Tuesday of a given week?

• 20%

• 48%

• 70%

• 98%

A sack contains the 26 letters of the alphabet, each printed on a separate wooden tile. You randomly draw one letter, REPLACE IT, and then you randomly draw a second letter.

Find the probability that the first letter drawn is T and the second letter drawn is A.

• $\frac{1}{26}$

• $\frac{1}{650}$

• $\frac{1}{464}$

• $\frac{1}{676}$

A sack contains the 26 letters of the alphabet, each printed on a separate wooden tile. You randomly draw one letter, you DO NOT replace it, and then you randomly draw a second letter.

Find the probability that the first letter drawn is P and the second letter drawn is S.

• $\frac{1}{26}$

• $\frac{1}{52}$

•  $\frac{1}{650}$ 

• $\frac{1}{676}$

A quality-control inspector checks for defective parts. The table shows the results of the inspector’s work. Find the probability that a defective part “fails”.

• $\frac{3}{39}$

• $\frac{36}{39}$

• $\frac{3}{461}$

• $\frac{36}{461}$