Question

An unusual number cube (with 6 sides) has the numbers 2, 2, 4, 4, 6, and 6 on its faces. It is rolled once. Match the outcome to its probability. 1. P(2 or 4) 1 2. P(multiple of 2) 2/3 3. P(multiple of 3) 1/3 4. P(odd prime numbers) 0

Answer 1

Below is the given columns whose entries are to be matched.

1. P(2 or 4) 1

2. P(multiple of 2) 2/3

3. P(multiple of 3) 1/3

4. P(odd prime numbers) 0

Let us solve this question by taking one entry at a time.

1. The probability of getting 2 or 4 is: P(2 or 4)=$\frac{2+2}{6}$=$\frac{4}{6}=\frac{2}{3}$

As there are 2 faces with 2 and 2 faces with 4 making the total number of required possible outcomes as 4, the making the probability $\frac{2}{3}$

2. We see that every number on the six faces of the cube is a multiple of 2 (2,4,6), thus, the probability of getting a multiple of 2 is 100% or in other words:

P(multiple of 2)=$\frac{6}{6}=1$

3. Likewise, Only 2 faces which have 6 are the multiples of 3, thus:

P(multiple of 3)=$\frac{2}{6} =\frac{1}{3}$

4. There is not a single prime number on the faces of the cube. Thus, there is not a single odd prime number on the faces of the cube.

Therefore, P(Odd Prime)=$\frac{0}{6}=0$

The above are the answers of the given question and the columns can thus be matched accordingly.