Text: Two events A and B are said to be independent if A. P(A/B) = 1 B. P(B/A) = 1 C. P(A/B) = P(A) D. P(A/B) = P(B) E. P(B/A) = P(A) Event A = You're on campus from 10:00 - 11:20 am today Event B = You're at home from 10:00 - 11:20 am today If we are interested in studying your location in this time period, Events A and B are: A. both mutually exclusive and collectively exhaustive B. collectively exhaustive C. mutually exclusive D. independent The probability of rolling a fair 6-sided die and tossing a fair coin and coming up with either a "5" or a "Heads" is: A. 0.50 B. 0.0833 C. 0.1667 D. 0.6667 E. 0.5833
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Consider the following two events that involve flipping a single coin and rolling one six-sided die. Complete parts a) and b) below: A = Coin comes up heads B = Rolling a five with the die a) Are these two events mutually exclusive? Why or why not? A. The events are not mutually exclusive. The event of the coin coming up heads cannot occur at the same time as rolling a five during the experiment. B. The events are mutually exclusive. The event of the coin coming up heads cannot occur at the same time as rolling a five during the experiment. C. The events are not mutually exclusive. The event of the coin coming up heads can occur at the same time as rolling a five during the experiment. D. The events are mutually exclusive. The event of the coin coming up heads can occur at the same time as rolling a five during the experiment. b) Are these two events independent? Why or why not? A. The events are dependent. The event of the coin coming up heads influences the probability of rolling a five. B. The events are independent. The event of the coin coming up heads influences the probability of rolling a five. C. The events are independent. The event of the coin coming up heads does not influence the probability of rolling a five. D. The events are dependent. The event of the coin coming up heads does not influence the probability of rolling a five.
Sri K.
Suppose events A and B are mutually exclusive. Event C is independent of A, and C is also independent of B. Assume P(A) = 1/4, P(B) = 1/3, and P(C) = 1/2. Let N denote the total number of events among A, B, C that occur. (a) Draw a Venn diagram by filling each disjoint part with a correct probability. (b) Choose one of the following answers for EN: 13/12; 2; 5/2. (c) Choose one of the following answers for E(N^2): 13/12; 5/3; 11/6. (d) Choose one of the following answers for Cov(IA, N): 0; 11/24; 5/48. (e) Choose one of the following answers for P(N <= 2 | C): 1; 5/24; 7/24.
Adi S.
Two events $E_{1}$ and $E_{2}$ are called independent if $p\left(E_{1} \cap E_{2}\right)=p\left(E_{1}\right) p\left(E_{2}\right) .$ For each of the following pairs of events, which are subsets of the set of all possible outcomes when a coin is tossed three times, determine whether or not they are independent. a) $E_{1} :$ tails comes up with the coin is tossed the first time; $E_{2} :$ heads comes up when the coin is tossed the second time. b) $E_{1} :$ the first coin comes up tails; $E_{2} :$ two, and not three, heads come up in a row. c) $E_{1} :$ the second coin comes up tails; $E_{2} :$ two, and not three, heads come up in a row. (We will study independence of events in more depth in Section $7.2 . )$
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