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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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Two similar pyramids have base areas of 12.2 cm2 and 16 cm2. The surface area of the larger pyramid is 56 cm2. What is the surfa
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Given =

Two similar pyramid have base area of 12.2 cm² and 16 cm².

surface area of the larger pyramid = 56 cm²

find out the surface area of the smaller pyramid

To proof =

Let us assume that the surface  area of the smaller pyramid be x.

as surface area of the larger pyramid is 56 cm²

Two similar pyramid have base area of 12.2 cm² and 16 cm².

by using ratio and proportion

we have

ratio of the base area of the pyramids : ratio of the surface area  of the pyramids

\frac{12.2}{16} : \frac{x}{56}

x = 12.2 ×56×\frac{1}{16}

by solvingthe above terms

we get

x =42.7cm²

Hence the surface area of the smaller pyramid be 42.7cm²

Hence proved










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