10. Suppose that eight cards are drawn from a 52-card deck. We are told that at leastthree of them are hearts. Let E be t event that the rest of them are also hearts.Compute P(E) by completing the following steps.(a) Let B be the event that at least three of the cards are hearts, and let A be theevent that all of the eight cards are hearts. Notice that P(A | B) = P(E).Compute P(An B).P(An B)(as a numerical approximation)(b) Now compute P(B). (Hint: Note that B = B3 UB4UB3U BU B6 U Bs whereB, is the event that that exactly i hearts where drawn. The B, are all disjoint.Compute P(B) for each i and add them up Write down the sum using Σ -notation, and then use WolframAlpha to compute the sum.)P(B)(as a fraction in lowest terms);P(E)=(as a fraction in lowest terms);(as a numerical approximation)(c) Combine your answers in parts (a) and (b) to compute P(E).(as a numerical approximation)9

10. Suppose that eight cards are drawn from a 52-card deck. We are told that at least three of them are hearts. Let E be the event that the rest of them are also hearts. Compute P(E) by completing the following steps. (a) Let B be the event that at least three of the cards are hearts, and let A be the event that all of the eight cards are hearts. Notice that P(A | B) P(E). Compute P(An B). P(An B) ܐܐ (as a fraction in lowest terms); (as a numerical approximation)

10. Suppose that eight cards are drawn from a 52-card deck. We are told that at least three of them are hearts. Let E be the event that the rest of them are also hearts. Compute P(E) by completing the following steps. (a) Let B be the event that at least three of the cards are hearts, and let A be the event that all of the eight cards are hearts. Notice that P(A | B) P(E). Compute P(An B). P(An B) ܐܐ (as a fraction in lowest terms); (as a numerical approximation)

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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2. Suppose that a single card is selected from a standard 52-card deck.A.) Compute the probability of the event E = “drawing a king.”B.) Compute the probability of the event E = “drawing a king” or F = “drawing a queen” or G = “drawing a jack.”3. Suppose that a pair of dice are thrown. Let A = “the first die is a 3”, let B = “the sum of the dice is less than or equal to 6”, let C = "the sum of the dice is 9", and let D = "the second die is a 5. Find the following:a.) P(A or D) b.) P(A and B) c.) P(A or B or D)d.) P[A or B or C)]Using the General Addition Rule.
B. A box contains 6 red balls 4 blue balls Draw two cards in a row If the draw is with return, what is the probability that 1. The two balls are blue 2. The two balls are of different colours
a. The Probaility of event A happening is P(A)-0.5. The probability of event B happening is I(B)-0.4. Considering these are both mutually exclusive events what is the probability of event A or eveat B occurring b. Dario owns 145 baseball cards, 102 football cards, and 4s basketball cards He selcets a card at randors and gives it to his brother. What is the probability that he selects a baseball or football card? I need quick help
) Suppose that events A and B are independent. Show that p(A | B) + p(B)(1-p(A)) - P(A ∪ B) = 0.
7. Three cards are drawn in succession, without replacement, From an Ordinary deck of playing cards. Find the probability that the event Cin C2 n Cs occurs, where C. is the event that +he First card is a l0 or a jack, and Co is the event that the third card is areater than 3 but less than red ace, Ca is the event that the second card is a 7.
Q6. Dr. Lawrence has three boxes. Their contents are Box 1: 2 red balls and 4 white balls Box 2: 4 red balls and 2 white balls Box 3: 3 red balls and 3 white balls First, a box is selected, and then two balls are drawn at random from that box (without replacement). a. What is the probability that the selected both balls are of the same color. b. If the selected balls are of the same color, what is the probability that they are selected from box 2?
Q. Two cards are drawn in succession without replacement from a ostandard 52-card deck. Compute the probability that (i) the second card is a red if the first card is the king of hearts; (ii) Both cards are black.
Suppose you roll 2 six-sided dice and sum the faces that show. Let A bethe event that the sum is less than or equal to 5, B be the event that the sum is even,and C be the event that the sum is greater than or equal to 8. Compute P(B | A) andP(C | A).
a) Show that for any three events A, B, and C, the probability that at least one of them occurs is P(A) + P(B) + P(C) - P(An B)- P(ANC) - P(BNC) + P(An BnC). b) Given A and B are independent events, with P(A) = 0.50 and P(B) = 0.30. Find P(ANB) c) About 52% of the residents of Capricorn municipality are happy and 48% of the residents are not happy with the delivery service. A recent study showed that 75% of happy residents and 25% of the unhappy residents are in favour of keeping the mayor of the municipality. If resident is randomly selected from the municipality residents is found to favour the motion. What is the probability that this person is happy with the delivery service?