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Chapter 15: Q7P (page 727)

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.

A letter is selected at random from the alphabet. What is the probability that it is one of the letters in the word 鈥減robability?鈥 What is the probability that it occurs in the first half of the alphabet? What is the probability that it is a letter after x?

Short Answer

Expert verified

The required sample space is a鈥鈥,鈥鈥b鈥鈥,鈥鈥c鈥鈥,鈥鈥鈰鈥鈥,鈥鈥z

The probability that the letter is one of the letters in the word 鈥減robability鈥 is 926.

The probability that the letter is occurs in the first half of the alphabet is 12

The probability that the letter is a letter after x is113.

Step by step solution

01

Definition of Probabilityof alphabets

It is known that there are 26 alphabets, this implies that for selecting a letter there are 26 total possible outcomes So, the probability of a letter is 126.

02

Determination ofthe probability that one of the letters in the word “probability”

There are 26 letters, this implies that for selecting a letter there are 26 total possible outcomes. So, the sample space is expressed as follows,

a鈥鈥,鈥鈥b鈥鈥,鈥鈥c鈥鈥,鈥鈥鈰鈥鈥,鈥鈥z

The probability of each letter is 126.

There is total 9 different letters in the word 鈥減robability鈥 namely p鈥鈥,鈥鈥r鈥鈥,鈥鈥o鈥鈥,鈥鈥b鈥鈥,鈥鈥a鈥鈥,鈥鈥i鈥鈥,鈥鈥l鈥鈥,鈥鈥t鈥鈥,鈥鈥y, this implies that the number of outcomes favourable are 9.

Find the probability that the letter is one of the letters in the word 鈥減robability鈥 adding the probabilities of each possible outcomes, that is 9 times 126.

p=9脳126=926

Thus, the probability that the letter is one of the letters in the word 鈥減robability鈥 is126.

03

Determination ofthe probability that it occurs in the first half of the alphabet

The first half of the alphabet series has 13 letters, this implies that the number of outcomes favourable are 13 and total number of outcomes are 26.

Find the probability that the letter is occurs in the first half of the alphabetby adding the probabilities of each possible outcomes, that is 13 times 126.

p=13脳126=12

Thus, the probability that the letter is occurs in the first half of the alphabet is12

04

 Step 4: Determination of the probability that it is a letter after x

It can be observed that there are only 2 letters after 鈥渪鈥 namely 鈥測鈥 and 鈥渮鈥, this implies that the number of outcomes favourable are 2 and total number of outcomes are 26.

Find the probability that the letter is a letter after x by adding the probabilities of each possible outcomes, that is 2 times 126.

p=2脳126=113

Thus, the probability that the letter is a letter after x is113

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Most popular questions from this chapter

Question: Use both the sample space (2.4) and the sample space (2.5) to answer the following questions about a toss of two dice.

(a) What is the probability that the sum is 鈮 4?

(b) What is the probability that the sum is even?

(c) What is the probability that the sum is divisible by 3?

(d) If the sum is odd, what is the probability that it is equal to 7?

(e) What is the probability that the product of the numbers on the two dice is 12?

(a) A weighted coin hasprobability23 ofcoming up heads and probability13of coming up tails. The coin is tossed twice. Let x = number of heads. Set up the sample space for x and the associated probabilities.

(b) Find x and 蟽.

(c)If in (a) you know that there was at least one tail, what is the probability that both were tails?

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?

Consider a biased coin with probability 13of headsand 23oftails and suppose it is tossed450times.

(a) Find the probability of getting exactly 320 tails.

(b) Find the probability of getting between 300 and 320 tails.

In paying a bill by mail, you want to put your check and the bill (with a returnaddress printed on it) into a window envelope so that the address shows right sideup and is not blocked by the check. If you put check and bill at random into theenvelope, what is the probability that the address shows correctly?
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