Exam 6: Some Rules of Probability

A school has tabulated the favorite snacks of 1000 of its students in the two categories, males and females. Here are the results: If one of the terms in the table above is selected at random, find each of the following probabilities. - $P\left(Z \mid M^{\prime}\right)=$ _______

To calculate the probability that both of two events will occur, we would most likely use the conditional formula.

Two options an automobile buyer may purchase are air-conditioning $(C)$ and an automatic transmission $(T)$ . A dealer notes from his sales records that the probability of a buyer purchasing an automatic transmission is 0.60 and the probability that he purchased air-conditioning is 0.50 . The probability that the buyer bought air-conditioning if he bought an automatic transmission is 0.70 . -In the situation above, if a buyer purchased air-conditioning, find the probability that he bought an automatic transmission.

If $A$ is the event of rolling a 3 on a roll of a die and $B$ is the event of rolling at least a 3 on the second roll of the die, then the events $A$ and $B$ are independent.

In an experiment, persons are asked to pick a number from 10 to 18 , so that for each person the sample space is the set $S=\{10,11,12,13,14,15,16,17,18\}$ . If $A=\{10,11,15,16,17\}, B=\{10,12,14\}$ , and $C=\{14,16,18\}$ , list the elements of the sample space comprising each of the following events. - $A \cap C$

A school has tabulated the favorite snacks of 1000 of its students in the two categories, males and females. Here are the results: If one of the terms in the table above is selected at random, find each of the following probabilities. - $P\left(F \cap I^{\prime}\right)=$ _______

Given mutually exclusive events $C$ and $D$ for which $P(C)=0.61$ and $P(D)=0.34$ , find - $P\left(D^{\prime}\right)$ .

Two options an automobile buyer may purchase are air-conditioning $(C)$ and an automatic transmission $(T)$ . A dealer notes from his sales records that the probability of a buyer purchasing an automatic transmission is 0.60 and the probability that he purchased air-conditioning is 0.50 . The probability that the buyer bought air-conditioning if he bought an automatic transmission is 0.70 . -In the situation above, find the probability that a buyer purchased both an automatic transmission and air-conditioning.

If $P(A)=\frac{2}{5}$ and $P(B)=\frac{4}{5}$ , then $P(A \cup B)$ must be greater than 1 .

The expression $P(A \cap B)=P(A) P(B \mid A)$ is valid if

Three families A, B, and C, are bidding on the same one -family house. The probabilities are $0.20,0.25$ , and 0.28 , respectively, that a given family eventually moves into the house. -In the situation above, find the probability that either family A or C eventually moves into the house.

A company has discovered a way of evaluating the success of both their radio and television advertising. If $R$ and $T$ are, respectively, the events that the radio advertising and television advertising are successful, $P(R)=0.62, P(T)=0.75$ , and $P(R \cap T)=\mathbf{0 . 4 3}$ . -Using the situation above, state in words what probability is expressed by the following: $P(R \cup T)$ .

If $A$ is the event that a product will be a financial success and $B$ is the event that production will be preceded by a marketing study, then the probability that the product will be a financial success if production will be preceded by a marketing study can be expressed symbolically as _______.

The events of drawing a ten and a jack on a single draw of one card from an ordinary deck of 52 cards are independent events.

A school has tabulated the favorite snacks of 1000 of its students in the two categories, males and females. Here are the results: If one of the terms in the table above is selected at random, find each of the following probabilities. - $P\left(F^{\prime} \mid Z^{\prime}\right)=$ _______

A school has tabulated the favorite snacks of 1000 of its students in the two categories, males and females. Here are the results: If one of the terms in the table above is selected at random, find each of the following probabilities. - $P\left(M \cap I^{\prime}\right)=$ _______

-Using Table 3, the probability that a person is both male and a teacher is _______.

A consumer has placed two orders for a new product from two different suppliers $X$ and $Y$ . The probabilities that the suppliers deliver the product on time are 0.40 for $X$ and 0.60 for $Y$ .45) If the probability of one supplier delivering the product on time has no effect on whether or not the other one does, find the probability that one or both of the suppliers will deliver the product in the required time. -If $X$ is the event that supplier $X$ delivers the product on time, and $Y$ is the event that supplier $Y$ delivers on time, the events $X$ and $Y$ are:

Given mutually exclusive events $C$ and $D$ for which $P(C)=0.61$ and $P(D)=0.34$ , find - $P\left(C^{\prime} \cap D^{\prime}\right)$ .

A school has tabulated the favorite snacks of 1000 of its students in the two categories, males and females. Here are the results: If one of the terms in the table above is selected at random, find each of the following probabilities. -=\) _______