Question

chapter 4.2 homework score: 69/83 answered: 36/38 question 38 4.2 theoretical probability. mutually exclusive/not mutually exclusive. determine whether the event described is mutually exclusive or not. then determine the probability of the event. type these as fractions. a) a die is rolled. what is the probability of rolling 5 or 4? choose: select an answer probability: b) a die is rolled. what is the probability of rolling at least 4? choose: select an answer probability: c) a card is drawn from a standard deck of cards. what is the probability of drawing 10 or jack? choose: select an answer probability: d) a card is drawn from a standard deck of cards. what is the probability of drawing king or spade? choose: select an answer probability:

Explanation:

Step1: Recall probability formula

The probability of an event $P(E)=\frac{n(E)}{n(S)}$, where $n(E)$ is the number of elements in the event - set and $n(S)$ is the number of elements in the sample - set. For a die, $n(S) = 6$, and for a standard deck of cards, $n(S)=52$.

Step2: Analyze part a

When rolling a die, the events of rolling a 5 and rolling a 4 are mutually exclusive. $n(E) = 2$ (either 4 or 5). So $P=\frac{2}{6}=\frac{1}{3}$.

Step3: Analyze part b

When rolling a die, the event of rolling at least 4 means rolling 4, 5, or 6. $n(E)=3$. So $P = \frac{3}{6}=\frac{1}{2}$.

Step4: Analyze part c

When drawing a card from a standard deck, the events of drawing a 10 and drawing a Jack are mutually exclusive. There are 4 tens and 4 Jacks. So $n(E)=4 + 4=8$, and $P=\frac{8}{52}=\frac{2}{13}$.

Step5: Analyze part d

When drawing a card from a standard deck, the event of drawing a King or a Spade is not mutually exclusive. There are 4 Kings and 13 Spades, but the King of Spades is counted twice. So $n(E)=4 + 13-1 = 16$, and $P=\frac{16}{52}=\frac{4}{13}$.

Answer:

a. Mutually Exclusive, $\frac{1}{3}$
b. Not Mutually Exclusive, $\frac{1}{2}$
c. Mutually Exclusive, $\frac{2}{13}$
d. Not Mutually Exclusive, $\frac{4}{13}$