See picture for question details ### Problem StatementEach of the digits 0-9 is written on a slip of paper, and the slips are placed in a hat. If 2 slips of paper are selected at random, determine the probability that the 2 numbers selected are greater than 3.The problem is to be done without replacement. Use combinations to determine the probability.The probability is ____ . (Type an integer or a simplified fraction.)---**Explanation:**To solve this problem, we need to calculate the probability that both numbers selected from the hat are greater than 3. Let's break down the steps:1. **Identify the total number of possible outcomes:** - There are 10 digits (0-9) written on slips and placed in a hat. - We are selecting 2 slips out of these 10, so the number of possible combinations (total outcomes) is given by the combination formula \( \binom{n}{k} \), where \( n \) is the total number of items, and \( k \) is the number of items to choose. - Total combinations = \( \binom{10}{2} = \frac{10!}{2!(10-2)!} = \frac{10 \times 9}{2 \times 1} = 45 \).2. **Identify the favorable number of outcomes:** - We need to find the number of combinations that yield numbers greater than 3. The digits greater than 3 are 4, 5, 6, 7, 8, and 9 (a total of 6 digits). - We are selecting 2 slips out of these 6, so the number of favorable combinations is \( \binom{6}{2} = \frac{6!}{2!(6-2)!} = \frac{6 \times 5}{2 \times 1} = 15 \).3. **Calculate the probability:** - The probability of selecting 2 numbers both greater than 3 is the number of favorable outcomes divided by the total number of possible outcomes: \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{15}{45} = \frac{1}{3} \]So the probability is \( \frac{1}{3} \).

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Description: See picture for question details ### Problem StatementEach of the digits 0-9 is written on a slip of paper, and the slips are placed in a hat. If 2 slips of paper are selected at random, determine the probability that the 2 numbers selected are great

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Algebra

Each of the digits 0-9 is written on a slip of paper, and the slips are placed in a hat. If 2 slips of paper are selected at random, determine the probability that the 2 numbers selected are greater than 3. The problem is to be done without replacement. Use combinations to determine the probability. The probability is (Type an integer or a simplified fraction.)

Each of the digits 0-9 is written on a slip of paper, and the slips are placed in a hat. If 2 slips of paper are selected at random, determine the probability that the 2 numbers selected are greater than 3. The problem is to be done without replacement. Use combinations to determine the probability. The probability is (Type an integer or a simplified fraction.)

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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