Answer to Question #151131 in Statistics and Probability for merry

Question

From a box containing 2 apples, 2 peaches and 2 oranges, 3 fruits are drawn at
random. Let P be a random variable representing the number of oranges that occur. Construct a probability distribution.

Answer 1

The most efficient way to solve this task is to list all possible combinations. We have 2 apples (a), 2 peaches(p) and 2 oranges (o). Let's write all possible combinations of tree fruits (order here doesn't matter)

1a 1p 1o

2a 1p

2a 1o

1a 2p

1a 2o

2o 1a

2o 1p

7 combinations in total.

To built probability distribution, we need to find following probabilities P(P=0), P(P=1), P(P=2). P=3 and more is not possible, because we have only 2 oranges.

Let's assign P value to every combination:

1a 1p 1o P=1

2a 1p P=0

2a 1o P=1

2p 1a P=0

2p 1o P=1

2o 1a P=2

2o 1p P=2

$\displaystyle P(P=0) = \frac{2}{7}$ because there 2 combinations with P=0 out of 7

$\displaystyle P(P=1) = \frac{3}{7}$

$\displaystyle P(P=2) = \frac{2}{7}$

So, the probability distribution is

value of P P=0 P=1 P=2

probability 2/7 3/7 2/7