Question

A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events: ????:{ One of the balls is yellow } ????:{ At least one ball is red } ????:{ Both balls are green } ????:{ Both balls are of the same color }

Answer 1

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

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