madeline rolls two six - sided dice. the probability of getting a specific number on either of the six…

madeline rolls two six - sided dice. the probability of getting a specific number on either of the six - sided dice is independent. what is the probability of rolling a four and a five? round your answer to four decimal places.

madeline rolls two six - sided dice. the probability of getting a specific number on either of the six - sided dice is independent. what is the probability of rolling a four and a five? round your answer to four decimal places.

Answer

Explanation:

Step1: Calculate the probability of getting a 4 on one die and 5 on the other

The probability of getting a 4 on one die and 5 on the other can happen in two ways: (4 on first die and 5 on second die) or (5 on first die and 4 on second die). The probability of getting a 4 on a single six - sided die is $P(4)=\frac{1}{6}$, and the probability of getting a 5 on a single six - sided die is $P(5)=\frac{1}{6}$. Since the events are independent, the probability of (4 on first die and 5 on second die) is $P_1=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$. The probability of (5 on first die and 4 on second die) is $P_2=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Step2: Calculate the total probability

The total probability $P = P_1+P_2$. $P=\frac{1}{36}+\frac{1}{36}=\frac{2}{36}=\frac{1}{18}\approx0.0556$

Answer:

0.0556