91影视

We are given that a set of $10$cards consists of$5$red cards and 5 black cards, the cards are shuf铿俥d thoroughly, we choose one out of those at random, observe the color, and replace it into the set, cards are thoroughly reshuf铿俥d, again choose a card at random, observe its color, and replace it in the set, it is done a total of four times. Here $X$be the number of red cards observed in these four trials

We need to find that random variable $X$

We will find random variable $X$. For that it is given that cards are shuf铿俥d thoroughly, and you choose one at random, observe its color, and replace it in the set .Now we will find probability for different cards.

There are total of $10$cards out of which$5$are red and$5$are black ; so probability of red is $\frac{1}{2}=0.5$

,Similarly for black it is $0.5$.

Now cards are thoroughly reshuf铿俥d, again we will choose a card at random, observe its color, and replace it in the set, it is done a total of four times , so probability of red and black would be exact.

It is given that $X$be the number of red cards observed in these four trials , so this would be binomial experiment.

So, answer is binomial distribution with $n=4$and $p=0.5$