Considering the experiment of tossing a pair of fair dice. Define event A and B as follows: A = event where no. of dots on the 1st toss is greater than or equal to the no. of dots on the 2nd toss B = event where no. of dots on the two tosses are both greater than 3  -Specify events A and B by roster method. Denote an outcome by an ordered pair, (x,y), where x  is the no. of dots on the first toss and y is the no. of dots on the second toss. -Compute for their a priori probabilities. Present answer as a fraction. Do not simplify.

Q: Two fair 6-sided dice are rolled. Let A = the event that the dice add to 7, and let B = the event…

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Q: Find the probability of the following events.

A: here as per policy i HERE USE BASIC PROBABILITY DEFINITION probability =no. of favourable…

Q: You have two fair dice, one white and one blue, are tossed. Explain whether the following pairs of…

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Q: Let A and B are two event of a sample space S and let P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.9 Are A…

A: We will use the union formula: P(A∪B)=0.9 P(A)+P(B)-P(A∩B)=0.9 0.5+0.7-P(A∩B)=0.9 P(A∩B)=0.5+0.7-0.9…

Q: Two fair (six-sided) dice are rolled, one blue and one red. Let A: "Sum of 8", and let B: "Red die…

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Q: Q4: b) You have two fair dice, one white- and one blue, are tossed. Explain whether the following…

A: Given, two fair dice : 1 white and 1 blue

Q: Let A, and A, be two events such that P[A] = 1/2. P[A2] = 3/5 and P[A2|A1] = 2/5 Then: %3D O PLA, n…

A: Solution: From the given information,

Q: Q2:Two dice are thrown together. Let A be the event getting less than 3 (A2) on the second die. Are…

A: Given that Two dice are thrown together. Sample space=S={(1,1), (1,2), (1,3), (1,4), (1,5), (1,6),…

Q: ) Let A and B be two events such that P(A)=0.9, P(B)-0.5, and P (A U B) =0.6. Find: a) P(AnB) b)…

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Q: Suppose that E and F are two events and that N(E and F)=340 and N(E)=720. What is P(FIE)? P(FIE)…

A: Given,N(E and F) = 340N(E) = 720Using formula,

Q: Suppose that E and F are two events and that N(E and F)=380 and N(E)=850. What is P(FIE)? P(FIE)…

A: We have given that N(E and F) = 380 N(E) = 850 We have to find P(F/E) = ?

Q: a) Are events F and H disjoint? Explain. |

A: Two events A and B are said to be disjoint if P(A and B) = 0

Q: 10. Two dice are rolled yet again. Define the following two events A = the sum of the faces is six,…

A: Two dice are rolled. So total number of sample points is 36.

Q: The Am supply and deman for various blood types. They estimate that about 45% of the U.S. population…

A: Type o = 45%  P(o)= 0.45  Type A = 40%  P(A)= 0.40  Type B = 11%  P(B)=0.11 Type AB = 100-(45+40+11)…

Q: Suppose you roll a pair of dice. Let A be the event that you observe an even number. Let B be the…

A: Set A contains {2,4,6,8,10,12) Set B contains {8,9,10,11,12} Let S contain all the events…

Q: A fair dice is rolled and the incoming face of the dice is recorded. Events A, B A = {dice greater…

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Q: (a) Find the probability of the event that two faces are the same without the information given. (b)…

A: The events E is defined as E = two faces are the same

Q: An experiment consists of rolling two fair dice and adding the dots on the two sides facing up. Find…

A: Sample space of rolling two dice: s=(1,1)(1,2)(1,3)(1,4)(1,5)(1,6)(2,1)(2,2)(2,3)(2,4)(2,5)(2,6)…

Q: Two dice are rolled.  (a) write out a sample space (b) find the probability of getting a sum of 6 or…

A: Given that ; Two dice are rolled.  A dice contains 6 digits i.e. { 1,2,3,4,5,6} Here we use basic…

Q: 8. Let P(A) = .35 and P(E)= .44. Also, events A and E are: mutually exclusive. Find a. P(ANE)…

A: Answer: From the given data, P(A) = 0.35 P(E) = 0.44 Events A and E are mutually exclusive

Q: Consider the two events below.  are they mutually exclusive?  Explain A fair die is rolled Event…

A: Concept: Two events are said to be mutually exclusive or disjoint if both events cannot occur at the…

Q: If A and B are two events of a sample space then p(A)=0.2 and p(B)=0.6 a d p(A/B)=0.5 then P(A/B)=

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Q: For two events, A and B, we have P(A) = 0.85, P(B) = 0.65, and P(AUB) = 0.9. Then, the value for…

A: P(A)  = 0.85  P(B) = 0.65  P(A∪B) = 0.9P(B|A) = ?

Q: Before using these variance estimates, what must we calculate?

A: Before using any variance estimate we should check whether it is biased or unbiased and calculate…

Q: Two dice are thrown. The events A, B, and C are as follows A: getting an even number on the first…

A: We have to describe all the events....

Q: 3 A bag contains 8 identical balls, but with different colors three blue balls, four red and one…

A: A bag contains 8 identical balls, but with different colors three blue balls, four red and one…

Q: Let a pair of fair dice be tossed. If the sum of obtained values is 6 the probability that one of…

A: From the provided information, A pair of fair dice be tossed. Total outcomes = 36

Q: b) Let A and B are two events such that: P(A) 0.5, P(B) 0.7, and P(AC n BC) = 0.2, use a Venn…

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Q: Determine the probability. 3) Assume events A, B are independent. a) Suppose the probabity of event…

A: Let A and B be are two independent events.

Q: Determine P(A and B)

A: Here given A red and white die are tossed  Total outcomes 36

Q: Use the data in the following table, which lists drive-thru order accuracy at popular fast food…

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Q: Consider tossing 1 dice with the following events A: roll a 4 or less, B: roll a 3 or less.  Are…

A: A tossing a die , the sample space is : S={1,2,3,4,5,6} n(S)=6 Event A : roll a 4 or less.…

Q: Let A and B are two event of a sample space S and let P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.9. Find…

A: We have given that  P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.9 P(A and B) = P ( A ∩ B)

Q: Let A and B are two event of a sample space S and let P(A) = 0.5, P(B) = 0.7 and P(AUB) = 0.9 .…

A: For any two events A and B, it is known that P(A ∪ B) = P(A)  + P(B) – P(A ∩ B).

Q: An experiment involves rolling a pair of dice and recording the numbers that come up. Describe the…

A: Take for example the assumption that the possible outcomes when the die is thrown are 1, 2, 3, 4, 5,…

Q: B: If we throw piece of dice (two) times, the event(A) represent appearance of two sides are…

A: Solution :  Given : Throw of piece of dice two times  ∴ n(S) = 36 Let, Event A : Appearance of two…

Q: Two fair dice are tossed, one red and one green. Let A be the event that the sum of the two dice is…

A: The theory of probability has its origin in the seventeenth century.The king of France who…