A box contains 10 balls numbered from 1 to 10 inclusive. If Ann remove

For Ann or For Jane TOTAL cases = 10
For Ann favorable cases = 10
For Ann probability of picking the ball = 10/10 = 1
Now that she has replaced the ball TOTAL cases remains the same.
For Jane favorable case = 1 (If annhad picked the ball number 2, then jane has to pick only that ball, so only one choice for jane, hence only one fav case)

Probability for Jane picking the same ball = 1/10.
D is the right answer

Since Ann can pick any ball and Jane has only a 1/10 chance to match it, the probability that they select the same ball is:

1 x 1/10 = 1/10

Alternate Solution:

Many students think that the answer is 1/10 x 1/10 = 1/100, thinking that each woman has a 1/10 probability of picking a particular ball. Let’s look at the “long” solution to this problem to clarify the correct answer of 1/10.

Consider the ball marked “1.” The probability that Ann picks this ball is 1/10, and so the probability that Jane also picks this ball is 1/10. The probability that both women will pick the ball marked “1” is, therefore, 1/10 x 1/10 = 1/100.

Now consider the ball marked “2.” Again, the probability that Ann picks this ball is 1/10, and the probability that Jane also picks this ball is 1/10. Thus, the probability that both women will pick the ball marked “2” is, 1/10 x 1/10 = 1/100.

We continue this for the balls marked 3, 4, 5, 6, 7, 8, 9, and 10. For each ball, the probability will be 1/100.

Since there are 10 balls, the probability that Ann and Jane will pick the same ball is, therefore, 10 x 1/100 = 10/100 = 1/10.

Answer: D

P(Ann and Jane remove same ball) = P(Ann removes ANY ball AND Jane's ball matches Ann's ball)
= P(Ann removes ANY ball) x P(Jane's ball matches Ann's ball)
= 1 x 1/10
= 1/10

Answer: D

Aside: Once Jane removes her ball (and then replaces it), we have 10 balls, and 1 of them is the one that Jane picked.
So, P(Jane's ball matches Ann's ball) = 1/10

Cheers,
Brent

Ways to choose for Ann = 10/10 = 1.
When this one is placed again in the box, the total number of balls in the box still remains 10.
So, Jane has only one chance to select a ball out of 10 balls.
Jane can choose = 1/10.
So the probability will be 1 x (1/10) = 1/10
Cheers!!

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