Question

From a box containing 2 apples, 2 peaches and 2 oranges, 4 fruits are drawn at random. Let P be a random variable representing the number of oranges that occur. Construct a probability distribution.

Answer 1

Solution:

Number of apples = 2

Number of peaches = 2

Number of oranges = 2

Total fruits = 6

4 fruits are random.

Let P be the random variable representing the number of oranges that occur.

So, P = {0, 1, 2}

When P = 0,

$P(0)=\dfrac{^2C_0\times ^4C_4}{^6C_4}=\dfrac1{15}$

When P = 1,

$P(1)=\dfrac{^2C_1\times ^4C_3}{^6C_4}=\dfrac{2\times 4}{15}=\dfrac8{15}$

When P = 2,

$P(2)=\dfrac{^2C_2\times ^4C_2}{^6C_4}=\dfrac{6}{15}=\dfrac2{5}$

Required probability distribution is:

P P(P)

0 $\dfrac1{15}$

1 $\dfrac8{15}$

2 $\dfrac2{5}$