Hallie is trying to win the grand prize on a game show. Should she try her luck by spinning a wheel with 6 equal sections labeled 1 to 6 and hope she gets a 5, or should she roll two number cubes and hope she gets the same number on both cubes? Explain.
I think that they are equal and both have the probability of 1/6 but can't figure out how to explain it.
Talk first about the spinner, then about the numbered cubes : )\
The spinner...
The number 5 occurs once on the spinner, so the probability is 1 in 6 chance of landing on the 5.
The probability is 1/6
The Pair of Dice...
first way p = 1/6
second way
the probability of getting some number the first time is one and the probability of getting that same number the second time is 1/6
1 * 1/6 = 1/6
So six of one, half dozen of the other
that's the answer
To determine which option, spinning the wheel or rolling the cubes, has a higher probability of winning the grand prize, we need to calculate the probabilities for each scenario.
1. Spinning the wheel:
The wheel has 6 equal sections labeled 1 to 6. Since Hallie is hoping to get a 5, there is only one favorable outcome (getting a 5) out of the 6 possible outcomes. Therefore, the probability of winning by spinning the wheel is 1 out of 6, or 1/6.
2. Rolling two number cubes:
When rolling two number cubes, each cube has 6 possible outcomes (numbers 1 to 6). To calculate the probability of getting the same number on both cubes, we need to determine the number of favorable outcomes (getting the same number) out of all the possible outcomes.
There are 6 distinct pairs of the same number: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6). Therefore, there are 6 favorable outcomes out of the total of 36 possible outcomes (6 outcomes on the first cube multiplied by 6 outcomes on the second cube).
Hence, the probability of winning by rolling two number cubes and getting the same number is 6 out of 36, or 6/36, which can be simplified to 1/6.
In conclusion, both options have an equal probability of winning the grand prize, with a probability of 1/6.