Question

1.Which events are dependent? I. flipping a coin multiple times II. picking even numbers, with replacement III. picking odd numbers, without replacement

2. Which events are independent?

I. flipping a coin multiple times
II. picking coins, with replacement
III. picking coins, without replacement

3.A spinner numbered 1 through 10 is spun 3 times.
What is the probability of spinning a 5, then an even number, and then another even number?
4. WriA bag contains 3 red, 5 brown, and 4 yellow potatoes.
What is the probability of randomly choosing 2 yellow potatoes without replacement?
Write your answer as a decimal.
Round to the nearest hundredth if neededte your answer as a decimal. Do not round.
5.What is the probability of getting heads, tails, and heads, in that order, when flipping a coin? Are these events dependent or independent?

A)1/6 dependent
B)1/6 independent
C)1/8 depent
D)1/8 independent

Answer 1

1- iii only
2- i & ii
5- 1/8; independent

Answer 2

1) Option III

2) Option I and II

3) The probability of events is 2.5%.

4) The probability of events is
`(1)/(11)`

5) Option D

Explanation:

1) To find : Which events are dependent?

Dependent events are those which depends of first trial i.e, conditional.

I. and II. Flipping a coin or picking a number are not dependent.

The probability of the result is the same every time. It only changes if you leave out what you picked the first time, because then the total number of possibilities is different.

According to reasoning,

III. picking odd numbers, without replacement is dependent because you

don't replace what you draw the first time.

Therefore, Option III is correct.

2) To find : Which events are independent?

Independent events are those which is not dependent on each other.

By the same reasoning above, I. and II. are independent i.e, flipping a coin multiple times and picking coins, with replacement.

Therefore, Option I and II are correct.

3) Given : A spinner numbered 1 through 10 is spun 3 times.

To find : What is the probability of spinning a 5, then an even number, and then another even number?

Solution :

Total number of outcomes = {1,2,3,4,5,6,7,8,9,10}=10

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

Probability of spinning a 5 first time is
`(1)/(10)=0.1`

Probability of an even number (2, 4, 6, 8 or 10) the second time
`(5)/(10)=(1)/(2)=0.5`

Probability of an even number (2, 4, 6, 8 or 10) the third time
`(5)/(10)=(1)/(2)=0.5`

Probability of all 3 events
`0.1* 0.5* 0.5=0.025`

Therefore, The probability of events is 2.5%.

4) Given : A bag contains 3 red, 5 brown, and 4 yellow potatoes.

To find : What is the probability of randomly choosing 2 yellow potatoes without replacement?

Solution :

Total number of outcomes = 3+5+4=12

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

Probability of getting 1st yellow potato
`(4)/(12)=(1)/(3)`

Probability of getting 2nd yellow potato
`(3)/(11)`

Probability of choosing 2 yellow potatoes without replacement
`(1)/(3)* (3)/(11)=(1)/(11)`

Therefore, The probability of events is
`(1)/(11)`

5) To find : What is the probability of getting heads, tails, and heads, in that order, when flipping a coin?

Solution :

Total number of outcomes are {HHH, HHT, HTH, HTT, THH, THT,TTH,TTT}=8

Favorable outcome of getting heads, tails, and heads - HTH=1

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

Probability of getting of getting heads, tails, and heads

`P=(1)/(8)`

Flipping a coin is an independent event as event A is not dependent on event B.

Therefore, The probability of events is
`(1)/(8)` and independent.

So, Option D is correct.