Question

A bag contains 5 blue marbles, 4 red marbles, and 3 orange marbles. Mrs. Cox picks one without looking , replaces it and picks another one. What is the probability that she picks two that are not orange?

Answer 1

Answer:

P = 9/16

Step-by-step explanation:

In this question, we are asked to calculate the probability of Mrs Cox picking marbles that are not orange in color.

First, since we are dealing with the color orange and the rest according to the question, we can say that we have only two sets of marbles. The first set is the orange and that contains just 3 orange marbles. The second set contains 5 blue and 4 red marbles making a total of 9.

The probability of not selecting an orange is this; number of non orange marbles/total number of marbles

Total number of marbles is 12. The probability is thus 9/12 or3/4.

Now the probability of selecting a non orange marble twice without replacement is 3/4 * 3/4 = 9/16

Answer 2

Answer: The probability that an orange marble will not be selected after the two attempts is 9/16

Step-by-step explanation:

The total quantity of items in the box =

5blue + 4red + 3orange

= 12 items altogether

The probability of picking up a blue marble = the number of blue marbles/total number of marbles

= 5/12

The probability of picking up a red marble =

The number of red marbles in the box/the total number of marbles

= 4/12

The probability of picking an orange marble = The number of orange marbles in the box/the total number of marbles

= 3/12

Then if two balls are selected at random with replacement, the probability that an orange will not be picked = p(blue,red) + p(red,blue) + p(blue,blue) + p(red,red)

p(blue,red) = 5/12 × 4/12 = 5/36

p(red,blue) = 4/12 × 5/12 = 5/36

p(blue,blue) = 5/12 × 5/12 = 25/144

p(red,red) = 4/12 × 4/12 = 16/144 = 1/9

We then add up these separate probabilities:

5/36 + 5/36 + 25/144 + 1/9 = 9/16

ALTERNATIVELY,

Since the probability of selecting an orange marble is 3/12 and the joint probability of picking other marbles is 9/12, then the probability that an orange marble will not be picked after 2 attempts with REPLACEMENT =

P(other marbles) =

9/12 × 9/12

= 9/16

Therefore if the selection is done WITH REPLACEMENT, the probability that an orange marble will not be selected after the two attempts is 9/16