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Math

QuestionSally reads a 50-page book. Find the probabilities of landing on a specific page, odd/even pages, first, and last pages.

Studdy Solution

STEP 1

Assumptions1. The book has50 pages. . Each page is equally likely to be chosen when the book is opened at random.

STEP 2

We start by finding the probability of landing on a specific page. The probability of an event is calculated by dividing the number of favorable outcomes by the total number of outcomes. In this case, the favorable outcome is landing on a specific page, and the total number of outcomes is the total number of pages in the book.
(specific page)=Number of favorable outcomesTotal number of outcomes(\text{{specific page}}) = \frac{{\text{{Number of favorable outcomes}}}}{{\text{{Total number of outcomes}}}}

STEP 3

Plug in the values for the number of favorable outcomes (1, because we are looking for a specific page) and the total number of outcomes (50, because there are50 pages in the book).
(specific page)=150(\text{{specific page}}) = \frac{1}{50}

STEP 4

The probability of landing on a specific page when the book is opened at random is1/50.

STEP 5

Next, we find the probability of landing on an odd page. The number of favorable outcomes is the number of odd pages in the book. Since half of the pages in the book are odd (assuming the first page is odd), the number of favorable outcomes is25.
(odd page)=Number of favorable outcomesTotal number of outcomes(\text{{odd page}}) = \frac{{\text{{Number of favorable outcomes}}}}{{\text{{Total number of outcomes}}}}

STEP 6

Plug in the values for the number of favorable outcomes (25) and the total number of outcomes (50).
(odd page)=2550(\text{{odd page}}) = \frac{25}{50}

STEP 7

implify the fraction to find the probability of landing on an odd page.
(odd page)=2550=12(\text{{odd page}}) = \frac{25}{50} = \frac{1}{2}

STEP 8

The probability of landing on an odd page when the book is opened at random is1/2.

STEP 9

The probability of landing on an even page is the same as the probability of landing on an odd page, because half of the pages in the book are even.
(even page)=(odd page)=2(\text{{even page}}) =(\text{{odd page}}) = \frac{}{2}

STEP 10

The probability of landing on the first page or the last page is the same as the probability of landing on a specific page, because there is only one first page and one last page.
(first page)=(specific page)=50(\text{{first page}}) =(\text{{specific page}}) = \frac{}{50}(last page)=(specific page)=50(\text{{last page}}) =(\text{{specific page}}) = \frac{}{50}So, the probabilities are as follows- Specific page/50- Odd page/2- Even page/2- First page/50- Last page/50

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