Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orang

Question

Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it. (a) What is the probability that the first marble you draw is blue? (b) Suppose you drew a blue marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw? (c) Suppose you instead drew an orange marble in the first draw. If drawing with replacement, what is the probability of drawing a 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. Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it. (a) What is the probability that the first marble you draw is blue? (b) Suppose you drew a blue marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw? (c) Suppose you instead drew an orange marble in the first draw. If drawing with replacement, what is the probability of drawing a 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. Marbles in an urn. Imagine you have an urn containing 5 red, 3 blue, and 2 orange marbles in it. (a) What is the probability that the first marble you draw is blue? (b) Suppose you drew a blue marble in the first draw. If drawing with replacement, what is the probability of drawing a blue marble in the second draw? (c) Suppose you instead drew an orange marble in the first draw. If drawing with replacement, what is the probability of drawing a 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.

Explanation / Answer

a)probability that the first marble you draw is blue= 3/(5+3+2)=3/10=.3
b)Suppose you drew a blue marble in the first draw. If drawing with replacement, the probability of drawing a blue marble in the second draw= .3
because number of marbles remain same in with replacement
c)same probablity as before. since in with replacement ir doesnt matter which color marble you took in 1st draw.
d).3*.3=.09
e)yes. the two draws are independednt. because, the conditional probability of drawing blue ball is unaltered by the even in 1st draw.

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