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Math  /  Data & Statistics

QuestionYou roll a 6-sided die two times.
What is the probability of rolling a 5 and then rolling a number greater than 2?2 ? Simplify your answer and write it as a fraction or whole number. □\square Submit

Studdy Solution

STEP 1

1. The die is fair, meaning each face has an equal probability of landing face up.
2. The two rolls are independent events.

STEP 2

1. Determine the probability of rolling a 5 on the first roll.
2. Determine the probability of rolling a number greater than 2 on the second roll.
3. Calculate the combined probability of both events occurring in sequence.

STEP 3

Calculate the probability of rolling a 5 on a 6-sided die.
The probability is given by:
P(rolling a 5)=16 P(\text{rolling a 5}) = \frac{1}{6}

STEP 4

Identify the numbers greater than 2 on a 6-sided die: 3, 4, 5, and 6.
There are 4 favorable outcomes out of 6 possible outcomes.
Calculate the probability of rolling a number greater than 2:
P(rolling a number greater than 2)=46=23 P(\text{rolling a number greater than 2}) = \frac{4}{6} = \frac{2}{3}

STEP 5

Since the two events are independent, multiply their probabilities to find the combined probability:
P(rolling a 5 and then a number greater than 2)=16×23 P(\text{rolling a 5 and then a number greater than 2}) = \frac{1}{6} \times \frac{2}{3}
Calculate the result:
=1×26×3=218=19 = \frac{1 \times 2}{6 \times 3} = \frac{2}{18} = \frac{1}{9}
The probability of rolling a 5 and then rolling a number greater than 2 is:
19 \boxed{\frac{1}{9}}

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