A box has 6 red 5 green 8 blue ball what is probability that

A box has 6 red 5 green &8 blue ball. what is probability that all four of them are either red or any two out of the four are green if 4 ball are picked randomly

Solution

In the given situation, there can be only one of the two cases, that is, we can either pick all 4 red balls or any 2 green balls, but not both together.

Therefore, P(All 4 red or any 2 green) = P(All 4 red) + P(Any 2 green)

=⁶C₄/¹⁹C₄+ ⁵C₂*¹⁴C₂/¹⁹C₄ = 0.239

Explanation: For the first term in the sem, we are to choose 4 red balls out of 6 red balls for all of them to be red. We can choose any 4 balls in ¹⁹C₄ ways, which is why it is the denominator in both cases. In the second case, we have to choose two green balls out of 5, and two balls of a different colour, out of 14 balls. Adding these two probabilities gives us the result.