hi i really need help on how to solve these two problems, thank you so much!!!
the manager of a local bank observes how long it takes a customer to complete his transactions at the automatic bank teller.
a. describe an appropriate sample space for this experiment.
b. describe the event that it takes a customer between 2 and 3 minutes to complete his transactions.
2. what is the probability that a roulette ball will come to rest on an even number other than 0 or 00? (assume that there are 38 equally likely outcomes consisting of the numbers 1-36, 0, and 00)?
your first question is too vague for me
#2. There are 18 even numbers
so the prob(even) = 18/38 = 9/19
(note there would also be 18 odd numbers, for a prob(odd) = 9/19
but 9/19 + 9/19 = 18/19 which is not 1.
I once played this for about 1/2 hour by putting a chip on evens and a chip on odds. My win on one of them covered the loss on the other.
So I was breaking even for quite a while, and received free drinks while playing, until the 00 came up, at which point I lost both chips and quit. )
Sure, I can help you with both of these problems. Let's start with the first one:
a. To describe an appropriate sample space for this experiment, we need to consider all the possible outcomes or scenarios that can occur. In this case, the manager is observing how long it takes a customer to complete their transactions at the automatic bank teller. The sample space can be the set of all possible time durations for completing transactions, where each outcome is a specific duration. For example, the sample space could be {1 minute, 2 minutes, 3 minutes, ..., n minutes}, where n is the maximum duration observed.
b. To describe the event that it takes a customer between 2 and 3 minutes to complete their transactions, we need to identify which outcomes from the sample space fall within this range. In this case, the event can be represented as {2 minutes, 2.1 minutes, 2.2 minutes, ..., 2.9 minutes, 3 minutes}, where the customer completes their transaction in a duration between 2 and 3 minutes (inclusive).
Moving on to the second problem:
To find the probability that a roulette ball will come to rest on an even number other than 0 or 00, we need to determine the number of favorable outcomes and the number of possible outcomes.
The favorable outcomes in this case are the even numbers from 1 to 36, excluding 0 and 00. There are 18 even numbers, since every second number is considered even on the roulette wheel.
The total number of possible outcomes is given as 38, which includes the numbers 1-36, 0, and 00.
Therefore, the probability can be calculated by dividing the number of favorable outcomes by the number of possible outcomes:
Probability = (Number of favorable outcomes) / (Number of possible outcomes) = 18 / 38
Simplifying, the probability is approximately 0.47368, or about 47.37%.
I hope this helps! Let me know if you have any further questions.