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noname [10]
3 years ago
11

Coach Kennedy will roll a number cube, numbered 1-6, twice. What is the probability of rolling a number less than or equal to 2,

then rolling a prime number?
Mathematics
1 answer:
sesenic [268]3 years ago
5 0

Answer:

The probability of rolling a number less than or equal to 2, then rolling a prime number is \frac{1}{6}.

Step-by-step explanation:

The sample space of rolling a number cube, numbered 1 - 6 is:

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

The cube is rolled twice.

Denote the events as follows:

<em>A</em> = rolling a number less than or equal to 2 in the first roll

<em>B</em> = rolling a prime number in the second roll

The two events <em>A</em> and <em>B</em> are independent.

This is because the result of rolling the cube the second time will not be dependent on the result of the first roll.

Compute the value of P (A) as follows:

Favorable outcomes = {1, 2} = 2

P (A) = Favorable outcomes of <em>A</em> ÷ Total number of outcomes

        =\frac{2}{6}

        =\frac{1}{3}

Compute the value of P (B) as follows:

Favorable outcomes = {2, 3, 5} = 3

P (B) = Favorable outcomes of <em>B</em> ÷ Total number of outcomes

        =\frac{3}{6}

        =\frac{1}{2}

Compute the probability of rolling a number less than or equal to 2, then rolling a prime number as follows:

P(A\cap B)=P(A)\times P(B)

               =\frac{1}{3}\times \frac{1}{2}

               =\frac{1}{6}

Thus, the probability of rolling a number less than or equal to 2, then rolling a prime number is \frac{1}{6}.

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