Explanation Given: p = 1 2 Number of trials of the experiment is 6 . Number of successes is 3 . Approach: The expanded expression of C ( n , x ) is given as; C ( n , x ) = n ! x ! ( n − x ) ! If p is the probability of success of an event and q is the probability of failure of an event. Then, the relationship between p and q is given as: q = 1 − p The probability of x successes in n independent trials is given by, P ( X = x ) C ( n , x ) p x q n − x Such that, x = 0 , 1 , 2 , 3 ......... , n Here, X is the binomial random variable and the probability distribution of X is called a binomial distribution. Calculation: Calculate the value of q . Substitute 1 2 for p in the expression for q . q = 1 − 1 2 = 1 2 Write the binomial distribution expression to calculate the probability of at least three success of an event having six trials. P ( X ≥ 3 ) = P ( X = 3 ) + P ( X = 4 ) + P ( X = 5 ) + P ( X = 6 ) ( 1 ) Also, P ( X = x ) = C ( n , x ) p x q n − x = n ! x ! ( n − x ) ! p x q n − x ( 2 ) Calculate P ( X = 3 ) Substitute 6 for n , 3 for x , 1 2 for p and 1 2 for p in equation ( 2 ) . P ( X = 3 ) = 6 ! 3 ! ( 6 − 3 ) ! ( 1 2 ) 3 ( 1 2 ) 6 − 3 = ( 720 6 × 6 ) ( 1 8 ) ( 1 8 ) = 720 2304 = 5 16 Calculate P ( X = 4 ) Substitute 6 for n , 4 for x , 1 2 for p and 1 2 for p in equation ( 2 ) .

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

11th Edition

ISBN: 9781285464657

Author: Soo T. Tan

Publisher: Brooks Cole

See similar textbooks

Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear re…

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Videos

Question

Chapter 8.4, Problem 13E

To determine

The probability of at least three successes.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 8.4, Problem 12E

Chapter 8.4, Problem 14E

Students have asked these similar questions

If you are using chatgpt leave it I will downvote .

Temperature measurements are based on the transfer of heat between the sensor of a measuring device (such as an ordinary thermometer or the gasket of a thermocouple) and the medium whose temperature is to be measured. Once the sensor or thermometer is brought into contact with the medium, the sensor quickly receives (or loses, if warmer) heat and reaches thermal equilibrium with the medium. At that point the medium and the sensor are at the same temperature. The time required for thermal equilibrium to be established can vary from a fraction of a second to several minutes. Due to its small size and high conductivity it can be assumed that the sensor is at a uniform temperature at all times, and Newton's cooling law is applicable. Thermocouples are commonly used to measure the temperature of gas streams. The characteristics of the thermocouple junction and the gas stream are such that λ = hA/mc 0.02s-1. Initially, the thermocouple junction is at a temperature Ti and the gas stream at…

A body of mass m at the top of a 100 m high tower is thrown vertically upward with an initial velocity of 10 m/s. Assume that the air resistance FD acting on the body is proportional to the velocity V, so that FD=kV. Taking g = 9.75 m/s2 and k/m = 5 s, determine: a) what height the body will reach at the top of the tower, b) how long it will take the body to touch the ground, and c) the velocity of the body when it touches the ground.

Chapter 8 Solutions

Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition

Ch. 8.1 - What is a random variable? Give an example.Ch. 8.1 - Prob. 2CQ Ch. 8.1 - Prob. 3CQ Ch. 8.1 - Three balls are selected at random without...Ch. 8.1 - 2.A coin is tossed four times. Let the random...Ch. 8.1 - A die is rolled repeatedly until a 6 falls...Ch. 8.1 - Cards are selected one at a time without...Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The probability of at least three successes.

Solution Summary: The author explains that the probability of at least three successes is 0.656.

Concept explainers

Videos

The probability of at least three successes.

Want to see the full answer?

Chapter 8 Solutions