Question

a packe of cards conatins 4 red and 5 black cards. a hand of 5 cards is drawn without replacment. What is the proablity of all five black. of exactly three black?

Answer 1

Answer: Our required probability is 0.3387.

Step-by-step explanation:

Since we have given that

Number of red cards = 4

Number of black cards = 5

Number of cards drawn = 5

We need to find the probability of getting exactly three black cards.

Probability of getting a black card = $\dfrac{5}{9}$

Probability of getting a red card = $\dfrac{4}{9}$

So, using "Binomial distribution", let X be the number of black cards:

$P(X=3)=^5C_3(\dfrac{5}{9})^3(\dfrac{4}{9})^2\\\\P(X=3)=0.3387$

Hence, our required probability is 0.3387.