How many outcomes are in this situation

  • Thread starter kevinf
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In summary: So b) would be asking for the number of sequences where each choice is a unique bin number. However, because there are only 5 balls and each has a 1/5 probability of being in any bin, the answer is 5^10.
  • #1
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i just want to check if my answer is correct.

10 distinct balls are to be tossed, one at a time, intto 5 distinct bins. find the number of possible outcomes the following case.

a) an outcome records only the identity of the bin for each toss (no record of the ball tossed)

b) an outcome records the identity of each ball and its bin (no record of the order in which balls are tossed)

wouldn't the answer be 5^10? since each ball has 10 possible bins that it can be tossed into and there are 5 balls so 5^10?

for b would it be the same answer as a?

thanks
 
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  • #2
kevinf said:
i just want to check if my answer is correct.

10 distinct balls are to be tossed, one at a time, intto 5 distinct bins. find the number of possible outcomes the following case.

a) an outcome records only the identity of the bin for each toss (no record of the ball tossed)

b) an outcome records the identity of each ball and its bin (no record of the order in which balls are tossed)

wouldn't the answer be 5^10? since each ball has 10 possible bins that it can be tossed into and there are 5 balls so 5^10?

for b would it be the same answer as a?

thanks

You're correct.

An easy way to reason for this problem is to consider that:

a) Every ball is independent from the others
b) There are five choices per ball. (ie P(A) = 1/5)

Because of the independence P(A and B) = P(A)P(B)

If you didn't have independence then it would not work out this way.

Also you said there are 10 possible bins when there are only five. For each ball you only have 5 bins and a 1/5 probability for each ball to land in any bin for each bin assuming equally likely probability.
 
  • #3
kevinf said:
i just want to check if my answer is correct.

10 distinct balls are to be tossed, one at a time, intto 5 distinct bins. find the number of possible outcomes the following case.

a) an outcome records only the identity of the bin for each toss (no record of the ball tossed)

b) an outcome records the identity of each ball and its bin (no record of the order in which balls are tossed)

wouldn't the answer be 5^10? since each ball has 10 possible bins that it can be tossed into and there are 5 balls so 5^10?

for b would it be the same answer as a?

thanks

Hi Kevinf,

It's a matter of interpretation of the problem statement, but I agree with you on b) but not a). It seems to me that a) is asking for the number of sequences of 10 choices where you have 2 possibilities for each choice. For example, if the bins are A and B, a possible sequence would be ABBABBBAA.
 

1. How do you determine the number of outcomes in a situation?

The number of outcomes in a situation can be determined by using the fundamental counting principle. This principle states that if there are n possible outcomes for one event and m possible outcomes for a second event, then there are n x m possible outcomes for both events combined.

2. Can you give an example of a situation with multiple outcomes?

Yes, a simple example would be flipping a coin. There are two possible outcomes, heads or tails. Another example could be rolling a six-sided die, which has six possible outcomes, each corresponding to a different number.

3. Are there any situations where the number of outcomes is infinite?

Yes, there are some situations where the number of outcomes is infinite. For example, if you are flipping a coin continuously, there are infinite possibilities for the number of heads and tails that can occur.

4. Can the number of outcomes change in the same situation?

No, the number of outcomes in a situation is determined by the variables involved and will not change unless those variables change. For example, if you are flipping a coin, there will always be two possible outcomes, regardless of how many times you flip it.

5. How does the number of outcomes affect the probability of an event occurring?

The number of outcomes has a direct impact on the probability of an event occurring. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The more outcomes there are, the lower the probability of a specific outcome occurring.

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