Imagine You Have an Urn Containing 5 Red 3 Blue and 2

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Imagine you have an urn containing 5 red, 3 blue, and orange marbles in it: (a) What Is the probability that the first marble you draw is blue? (b) Suppose you drew blue marble in the first draw: If drawing with replacement, what is the probability of drawing blue marble in the second draw? (c) Suppose vou instead drew an orange marble in the first draw: If drawing with replacement; what is the probability of drawing blue marble in the second draw? (d) If drawing with replacement; what is the probability of drawing two blue marbles in a row? (e) When drawing with replacement, are the draws independent? Explain;

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Video Transcript

Hello everyone. We are going to solve the question. And this question we are given that there are 10 marbles in and on and red marbles are five to our orange and three are blue marbles. So in a pot we have to find probability that the marble withdrew is blue in color, marble is blue in color. So this is equals to the number of blue marbles which is three and divided by number of total marbles with just 10. This is equal to 0.3. So answer for first part That is the marble which we drew as blue in color is 0.3. So this is the answer for a part. Now moving on to the part to be in B. But we have to find that suppose we drew a blue marble in first row. Then if drawing with replacement, then what is the probability of obtaining the blue marble in second row? So if we draw a blue marble in first draw and then we replace this, we put that marble back, then the blue marbles and the total marble remains him. So the probability that second marble is blue after replacement After replacement. The number of marbles the same. So that means there are three blue marbles and 10 Total marble which is equals to 0.3. So the probability for be part Is equal to 2.3. So this is the answer for b. part. Now moving on to part C in C. But we have to find that if we drew orange marble in first row and with replacement, then what is the probability of drawing a blue marble? Again, it is same as we replace the orange marble. So the total marvin's well maintained and the blue marble remain three. So probability As equals to three divided by 10 with 0.3. So we have probability equals to 0.34 c. part. This is the correct answer. Now moving on to the party in the part we have to find if drawing with replacement. What is the probability that the two marbles are blue in color in a row. So we have to find probability blue marbles in a row that means to bloom are building a room. So Probability for first blue marble is .3, probability of second blue marble is .3 which is equal to 0.09. So the required probability in depart required probability Is equal through 0.09. Which was the final answer for departure. Now moving on to part C in C. But sorry in every part. When drawing with replacement. Are the drawers independent. We have to tell if we are replacing the marbles then the drawers are independent or not. Yes the drawers. The two drawers odd. Independent. Because the conditional probability conditional probability of drawing blue balls is unaltered is unaltered. Bye bye. The first to draw. So this is a final answer for everybody. Thank you

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