Examine the spinner below. Answer the following questions. a) What is the probab

Question

Examine the spinner below. Answer the following questions. a) What is the probability the arrow will land on a 4 or a 3. b) What rule and what formula did you use? c) What type of events are these? Explain. A note on decks of cards: A deck of cards consists of 52 cards. There are 13 cards for each of the four suits: clubs, spades, diamonds, and hearts. The 13 cards are numbered 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, Ace. Clubs and spades are black. Diamonds and hearts are red. A face card is a Jack, Queen, or King. (An Ace is NOT considered a face card. A single card is chosen at random from a standard deck of 52 cards. a) Find the probability that a spade or a queen is drawn. State the rule, show the formula setup with appropriate notation, perform the calculation, and then fraction into decimal form to 3 decimal places. b) Give and explain the two terms that apply to the above problem.

Explanation / Answer

19.

(a) There are 5 mutually exclusive events:

landing on 1,2,3,4 or 5.

By addition theorem of probability:

P(landing on 4 or 3) = P(landing on 4) + P(landing on 3) = 1/5 + 1/5 = 2/5 = 0.4

(b) Rule used is Addition Theorm for Mutually Exclusine events:
P(A+B)= P(A) + P(B), if A and B are mutually exclusive.

(c) The 5 events are mutually exclusibe, because no two events can occur together: The occurrence of one event prevents the occurrence of other 4 events in a single trial.

20.

(a) P(spade or queen) = P(spade) + P(queen) - P(spade & queen)

                                = 13/52 + 4/52 - 1/52

                                = 0.25 + 0.077 - 0.019

                                = 0.308

(b) In the above problem, generalised addition theorem is used:

P(A+B) = P(A) + P(B) - P(AB)

where, P(AB) is the probability of occurrence of both A and B.

Here A and B are not mutiually exlusive, i.e., the occurrence of A does not affect the occurrence of B in a single trial.

Thus, the two terms used in the problem are : (i) Generalized addition theorem and (ii) not mutully exclusive events. They have been explianed.

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