Chapter 15: Q11MP (page 777)
A die is thrown 720 times.
(a) Find the probability that3comes up exactly 125 times.
(b) Find the probability that 3 comes up between115and 130 times.
(a) The value required for part a is given below.
(b) The value required for part b is given below.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
A so-called 7-way lamp has three 60-watt bulbs which may be turned on one or two or all three at a time, and a large bulb which may be turned to 100 watts, 200 watts or300 watts. How many different light intensities can the lamp be set to give if the completely off position is not included? (The answer is not 7.)
A coin is tossed repeatedly; x = number of the toss at which a head first appears.
Two people are taking turns tossing a pair of coins; the first person to toss two alike wins. What are the probabilities of winning for the first player and for the second player? Hint: Although there are an infinite number of possibilities here (win on first turn, second turn, third turn, etc.), the sum of the probabilities is a geometric serieswhich can be summed; see Chapter 1 if necessary.
A thick coin has probability of falling heads, of falling tails, and of standing one edge. Show that if it is tossed repeatedly it has probability 1 of
Eventually standing on edge.
Given a non uniform sample space and the probabilities associated with the points, we defined the probability of an event A as the sum of the probabilities associated with the sample points favorable to A. [You used this definition in Problem 15with the sample space (2.5).] Show that this definition is consistent with the definition by equally likely cases if there is also a uniform sample space for the problem (as there was in Problem 15). Hint: Let the uniform sample space have n<Npoints each with the probability N-1. Let the nonuniform sample space have n points, the first point corresponding to N1 points of the uniform space, the second to N2 points, etc. What is N1 + N2 + .... Nn ?What are p1, p2, ...the probabilities associated with the first, second, etc., points of the nonuniform space? What is p1 + p2 +....+ pn? Now consider an event for which several points, say i, j, k, of the nonuniform sample space are favorable. Then using the nonuniform sample space, we have, by definition of the probability p of the event, p = pi + pj + pk . Write this in terms of the N’s and show that the result is the same as that obtained by equally likely cases using the uniform space. Refer to Problem 15as a specific example if you need to.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
