Question

Two apples are selected at random and removed in succession and without replacement from a bag containing five golden apples and three red apples. List the elements of the sample space, the corresponding probabilities, and the corresponding values of the random variable X; where X is the number of golden apples selected.

Answer 1

Number of golden apples = 5

Number of red apples = 3

Total number apples = 5+3 =8

2 Golden apples ,

Probability of selecting 2 golden apples

= Number of ways selecting 2 golden apples from 5 golden apples / Number of ways of selecting 2 apples from 8 apples

X=2

1 Golden apple 1 red apple

Probability of selecting 1 golden apple and 1 red apple

= Number of ways selecting 1 golden apples from 5 golden apples and number of ways of selecting 1 red apple from 3 red apples / Number of ways of selecting 2 apples from 8 apples

X=1

2 red apple

Probability of selecting 2 red apples

= Number of ways selecting 2 red apple from 3 red apples / Number of ways of selecting 2 apples from 8 apples

X=0