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Chapter 15: Q13MP (page 777)
A radioactive source emits particles during an observation lasting 10 hours. In how many one-minute intervals do you expectno? ?
The values required is given below.
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Set up an appropriate sample space for each of Problems 1.1 to 1.10 and use it to solve the problem. Use either a uniform or non-uniform sample space or try both.
A single card is drawn at random from a shuffled deck. What is the probability that it is red? That it is the ace of hearts? That it is either a three or a five? That it is either an ace or red or both?
Prove (3.1) for a nonuniform sample space. Hints: Remember that the probability of an event is the sum of the probabilities of the sample points favorable to it. Using Figure 3.1, let the points in A but not in AB have probabilities p1, p2, ... pn, the points in have probabilities pn+1, pn+2, .... + pn+k, and the points in B but not in AB have probabilities pn+k+1, pn+k+2, ....pn+k+l. Find each of the probabilities in (3.1) in terms of the 鈥檚 and show that you then have an identity.
The following measurements of and have been made.
Find the mean value and the probable error ofand.
Five cards are dealt from a shuffled deck. What is the probability that they are all of the same suit? That they are all diamond? That they are all face cards? That the five cards are a sequence in the same suit (for example, 3, 4, 5, 6, 7 of hearts)?
Set up an appropriate sample space for each of Problems 1.1 to 1.10 and use itto solve the problem. Use either a uniform or non-uniform sample space or try both.
You are trying to find instrument A in a laboratory. Unfortunately, someone has put both instruments A and another kind (which we shall call B) away in identical unmarked boxes mixed at random on a shelf. You know that the laboratory has 3 A鈥檚 and 7 B鈥檚. If you take down one box, what is the probability that you get an A? If it is a B and you put it on the table and take down another box, what is the probability that you get an A this time?
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