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ELEN [110]
3 years ago
12

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the followi

ng events: ????:{ One of the balls is yellow } ????:{ At least one ball is red } ????:{ Both balls are green } ????:{ Both balls are of the same color }
Mathematics
1 answer:
Stels [109]3 years ago
8 0

Answer:

One of the balls is yellow: 0.36

At least one ball is red:0.73

Both balls are green:0.3

Both balls are of the same color:0.266

Step-by-step explanation:

To get the probability equally likely of choosing balls we use the following formula

P=# of possibilities that meet the condition / #of equally likely possibilities.

#of equally likely possibilities of the first experiment is 1+2+3=6

#of equally likely possibilities of the second experiment is 1+2+3 -1 =5 ( no replacement)

We choose 2 balls so we have to multiple  or add the probability of the 2 experiments,  that depends on the case

One of the balls is yellow:

1 experiment P{ One of the balls is yellow }= 1/6

2 experiment P{ One of the balls is yellow }= 1/5

P{ One of the balls is yellow }= 1/6+1/5=11/30

At least one ball is red:

1 experiment P{ One of the balls is red }= 2/6

2 experiment P{ One of the balls is red }= 2/5

P{ One of the balls is yellow }= 2/6+2/5=22/30

Both balls are green:

1 experiment P{ Both balls are green }= 3/6

2 experiment P{ Both balls are green }= 3/5

P{ Both balls are green }= 3/6*3/5=0.3

Both balls are of the same color

1 experiment P{ Both balls are green }= 3/6

2 experiment P{ Both balls are green }= 2/5

P{ Both balls are green }= 3/6*2/5=0.2

1 experiment P{ Both balls are red }= 2/6

2 experiment P{ Both balls are red }= 1/5

P{ Both balls are red }= 3/6*3/5=0.066

Both could happens so we add the probabilities

P{ Both balls are of the same color }=0.2+0.066=0.266

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Answer:

ŷ = 739.49X + 4876.43

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X :

1

2

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6231

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Using the online linear regression calculator :

The linear trend :

ŷ = 739.49X + 4876.43

Where x = year

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The quadratic model:

General form:

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y = 6755.98 - 388.24x + 125.30x²

The exponential model:

y = AB^x

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B.) Next three years :

Year 2009 ; x = 9

Year 2010 ; x = 10

Year 2011 ; x = 11

Linear:

ŷ = 739.49(9) + 4876.43

y = 11531.8

Year 2010 ; x = 10

y = 739.49(10) + 4876.43

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Year 2011 ; x = 11

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Year 2009 ; x = 9

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y = 5428.98(1.09)^11

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