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spayn [35]
3 years ago
14

Tamara finds the sum of two number cubes rolled at the same time. The chart below shows all possible sums from the 36 possible c

ombinations when rolling two number cubes. How many times should Tamara expect the sum of the two cubes to be equal to 5 if she rolls the two number cubes 180 times?
Mathematics
1 answer:
lutik1710 [3]3 years ago
8 0

Answer:

Tamara should expect the sum of the two cubes to be equal to 5 20 times.

Step-by-step explanation:

The sample space of rolling a number cube are:

S = {1, 2, 3, 4, 5, 6}

If two such cubes are rolled together, then the sum of the two cubes will be 5 for the combinations below:

S₁ = {(1, 4), (2, 3), (3, 2) and (4, 1)}

The total number of outcomes will be, <em>N</em> = 36.

Compute the probability that the sum of rolling two numbered cubes as follows:

P(\text{Sum}=5)=\frac{4}{36}=\frac{1}{9}

Let <em>X</em> = number of time the sum of the two numbers on two cubes is 5.

Two numbered cubes are rolled <em>n</em> = 180 times.

The event of getting a sum of 5 in independent of the other results.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 180 and <em>p</em> = \frac{1}{9}.

The expected value of <em>X</em> is:

E(X)=np

Compute the expected number of times Tamara expects the sum of the two cubes to be equal to 5 as follow:

E(X)=np\\=180\times \frac{1}{9}\\=20

Thus, Tamara should expect the sum of the two cubes to be equal to 5 20 times.

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