Independent and Dependent Events

A bag contains five red marbles and three blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. Both the first and second marbles are red.

• 64/1331 ≈ 0.048

• 25/64 ≈ 0.391

• 56/225 ≈ 0.249

• 7/22 ≈ 0.318

You flip a coin twice. The first flip lands tails-up and the second flip also lands tails-up.

• 1/32 ≈ 0.031

• 1/4 = 0.25

• 1/22 ≈ 0.045

• 1/192 ≈ 0.005

A bag contains three red marbles and five blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. Both the first and second marbles are red.

• 6/91 ≈ 0.066

• 1/4 = 0.25

• 9/64 ≈ 0.141

• 21/55 ≈ 0.382

A bag contains eight red marbles and seven blue marbles. Another bag contains four green marbles and three yellow marbles. You randomly pick one marble from each bag. One marble is blue and one marble is yellow.

• 5/36 ≈ 0.139

• 1/5 = 0.2

• 1/96 ≈ 0.01

• 24/91 ≈ 0.264

A basket contains four apples and six peaches. You randomly select a piece of fruit and then return it to the basket. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second piece is a peach.

• 6/25 ≈ 0.24

• 1/4 = 0.25

• 10/39 ≈ 0.256

• 1/36 ≈ 0.028

A bag contains eight red marbles and eight blue marbles. Another bag contains six green marbles and three yellow marbles. You randomly pick one marble from each bag. One marble is blue and one marble is yellow.

• 1/64 ≈ 0.016

• 8/165 ≈ 0.048

• 1/81 ≈ 0.012

• 1/6 ≈ 0.167

A basket contains seven apples and four peaches. You randomly select a piece of fruit and then return it to the basket. Then you randomly select another piece of fruit. The first piece of fruit is an apple and the second piece is a peach.

• 1/17 ≈ 0.059

• 7/26 ≈ 0.269

• 1/1024 ≈ 0.001

• 28/121 ≈ 0.231

You roll a fair six-sided die five times. The die shows an even number the first two times and an odd number the remaining three times.

• 1/32 ≈ 0.031

• 10/39 ≈ 0.256

• 24/121 ≈ 0.198

• 1/192 ≈ 0.005

You flip a coin twice. The first flip lands heads-up and the second flip also lands heads-up.

• 36/121 ≈ 0.298

• 1/4 = 0.25

• 42/169 ≈ 0.249

• 5/49 ≈ 0.102

A bag contains six red marbles and five blue marbles. You randomly pick a marble and then return it to the bag before picking another marble. The first marble is red and the second marble is blue.

• 1/9 ≈ 0.111

• 30/121 ≈ 0.248

• 1/4 = 0.25

• 1/12 ≈ 0.083