sample probability

sample probability - Question 2: Two coins are tossed, find...

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Question 2: Two coins are tossed, find the probability that two heads are obtained. Note: Each coin has two possible outcomes H (heads) and T (Tails). Solution to Question 2: The sample space S is given by. S = {(H,T),(H,H),(T,H),(T,T)} Let E be the event "two heads are obtained". E = {(H,H)} We use the formula of the classical probability. P(E) = n(E) / n(S) = 1 / 4 Question 3: Which of these numbers cannot be a probability? a) -0.00001 b) 0.5 c) 1.001 d) 0 e) 1 f) 20% Solution to Question 3: A probability is always greater than or equal to 0 and less than or equal to 1, hence only a) and c) above cannot represent probabilities: -0.00010 is less than 0 and 1.001 is greater than 1. Question 4: Two dice are rolled, find the probability that the sum is a) equal to 1 b) equal to 4 c) less than 13 Solution to Question 4: a) The sample space S of two dice is shown below. 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) (3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
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(5,1),(5,2),(5,3),(5,4),(5,5),(5,6) (6,1),(6,2),(6,3),(6,4),(6,5),(6,6) } Let E be the event "sum equal to 1". There are no outcomes which correspond to a sum equal to 1, hence P(E) = n(E) / n(S) = 0 / 36 = 0 b) Three possible ouctcomes give a sum equal to 4: E = {(1,3),(2,2),(3,1)}, hence. P(E) = n(E) / n(S) = 3 / 36 = 1 / 12 c) All possible ouctcomes, E = S, give a sum less than 13, hence. P(E) = n(E) / n(S) = 36 / 36 = 1 Question 5: A die is rolled and a coin is tossed, find the probability that the die shows an odd number and the coin shows a head. Solution to Question 5: The sample space S of the experiment described in question 5 is as follows S = { (1,H),(2,H),(3,H),(4,H),(5,H),(6,H) (1,T),(2,T),(3,T),(4,T),(5,T),(6,T)} Let E be the event "the die shows an odd number and the coin shows a head". Event E may be described as follows E={(1,H),(3,H),(5,H)} The probability P(E) is given by P(E) = n(E) / n(S) = 3 / 12 = 1 / 4 Question 6: A card is drawn at random from a deck of cards. Find the probability of getting the 3 of diamond. Solution to Question 6:
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sample probability - Question 2: Two coins are tossed, find...

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