Question

17 multiple choice 2 points the faces of a cube are numbered from 1 to 6. what is the probability of not rolling a 5 on a single toss of this cube? $\frac{4}{5}$ $\frac{1}{6}$ $\frac{5}{6}$ $\frac{1}{5}$ 18 multiple choice 2 points selena and tracey play on a softball team. selena has 8 hits out of 20 times at bat, and tracey has 6 hits out of 16 times at bat. based on their past performance, what is the probability that both girls will get a hit next time at bat? $\frac{14}{36}$ $\frac{48}{320}$ 1 $\frac{31}{40}$

Explanation:

Step1: Calculate total outcomes and favorable outcomes for first problem

A cube has 6 faces. The total number of possible outcomes when rolling a cube is 6. The number of outcomes that are not 5 is 5.

Step2: Use probability formula for first problem

The probability formula is $P(A)=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So the probability of not rolling a 5 is $\frac{5}{6}$.

Step3: Calculate individual probabilities for second - problem

Selena's probability of getting a hit, $P(S)=\frac{8}{20}=\frac{2}{5}$. Tracey's probability of getting a hit, $P(T)=\frac{6}{16}=\frac{3}{8}$.

Step4: Use multiplication rule for independent events for second problem

Since the events of Selena and Tracey getting a hit are independent, the probability that both get a hit is $P(S\cap T)=P(S)\times P(T)=\frac{2}{5}\times\frac{3}{8}=\frac{6}{40}=\frac{3}{20}=\frac{48}{320}$.

Answer:

1. C. $\frac{5}{6}$
2. B. $\frac{48}{320}$