Learning Materials
Features
Discover
Chapter 15: Q15MP (page 777)
Out of 1095people, what is the probability that exactly 2 were born on Jan.1 ? Assume 365days in a year
The value of the function from binomial distribution is 0.224.
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
Suppose that Martian dice are 4-sided (tetrahedra) with points labeled . When a pair of these dice is tossed, let x be the product of the two numbers at the tops of the dice if the product is odd; otherwise.
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.
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.
If you select a three-digit number at random, what is the probability that the units digit is 7? What is the probability that the hundreds digit is 7?
Two dice are thrown. Use the sample space (2.4) to answer the following questions.
(a) What is the probability of being able to form a two-digit number greater than
33 with the two numbers on the dice? (Note that the sample point 1, 4 yields
the two-digit number 41 which is greater than 33, etc.)
(b) Repeat part (a) for the probability of being able to form a two-digit number
greater than or equal to 42.
(c) Can you find a two-digit number (or numbers) such that the probability of
being able to form a larger number is the same as the probability of being able
to form a smaller number? [See note part (a)]
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.
Explanations 
Textbooks 
Exams 
GCSE 
IGCSE 
AS 
A Level 
International A Level 
University Admissions Tests 
Flashcards 
Vaia AI 
Notes 
Study Plans 
Study Sets 
Find a job 
Find a degree 
Student Deals 
Magazine 
Mobile App