There are seven city council members, two of whom are contractors. Two council members are selected...

Question

Question

There are seven city council members, two of whom are contractors. Two council

members are selected at random to serve on the city Planning Commission. Calculate the

probability that the two contractors will be selected for the Planning Commission.

Answer 1

Answer #1

Total no of seven council members are there hence n =7 and out of which 2 are contracters

so, probability of selecting a contractor is 2/7=0.2857

Now if two members are selected at random then the no of ways these 2 can be selected are

C(7,2)

= L8BuDXNU+wERfDaRCCIRRCKASAQQiQAiEQDA3zvT

=21

Now by using binomial formula

Formula:

P (k successes in n trials) = (、. )pkqn_k p*q

n = number of trials
k = number of successes
p = probability of success in one trial
q = 1 – p = probability of failure in one trial

Probability calculated using above formula as 0.3187

Answer 2

Similar Homework Help Questions

A city council consists of seven democrats and eight republicans. if a committee of seven people...

A city council consists of seven democrats and eight republicans. if a committee of seven people is selected, find the probability lf selecting five democrats and two republicans
A city council consists of seven Democrats and seven Republicans. If a committee of six people...

A city council consists of seven Democrats and seven Republicans. If a committee of six people is selected, find the probability of selecting three Democrats and three Republicans.
1. The Taipei City Council has 11 members: 6 males, 5 females. They wish to form...

1. The Taipei City Council has 11 members: 6 males, 5 females. They wish to form a committee of 5. (a) (2 pts) How many ways can the city council form the committee? (b) (12 pts) Complete the probability distribution below: Number of Females x Probability of Number of Females P(x) 0 1 2 3 4 5 3 Number of females x Probability of Number of Females P(x) 0 1 2 3 4 5 (c) (5 pts) Find the probability...

5 9 10 11 12 13 14 A university's leadership council is made up of 13...

5 9 10 11 12 13 14 A university's leadership council is made up of 13 members: 4 are students, 5 are teachers, and 4 are deans. A newspaper reporter is planning to select two of the council members for interviews. The first member will be chosen at random, and then the second member will be chosen at random from the remaining members. What is the probability that two teachers will be selected? Report your answer as an exact fraction....
Membership selection. A town council has 13 members, 7 Democrats and 6 Republicans. (A) If the...

Membership selection. A town council has 13 members, 7 Democrats and 6 Republicans. (A) If the president and vice-president are selected at random, what is the probability that they are both Democrats? (B) If a 3-person committee is selected at random, what is the probability that Republicans make up the majority?
Should a local government allow elected city council members to manage, or should they be the...

Should a local government allow elected city council members to manage, or should they be the group that decides policy rather than manage the day-to-day affairs of the community?

5.2.7 A concerned city council member thinks that one of the neighborhoods in the city close...

5.2.7 A concerned city council member thinks that one of the neighborhoods in the city close to a nuclear power plant has an unusually high rate of cancer. For the whole city, the rate is 1%. Twenty households in that neighborhood are randomly selected, what is the probability that at least 1 household in that neighborhood has an occupant with cancer. Is this event unusual?
A committee has ten members. There are two members that currently serve as the board's chairman...

A committee has ten members. There are two members that currently serve as the board's chairman and vice chairman. Each member is equally likely to serve in any of the positions. Two members are randomly selected and assigned to be the new chairman and vice chairman. What is the probability of randomly selecting the two members who currently hold the positions of chairman and vice chairman and reassigning them to their current positions?
The city council consists of 7 republicans and 8 democrats. A committee of 5 councilpersons is...

The city council consists of 7 republicans and 8 democrats. A committee of 5 councilpersons is randomly selected. Find the probability that the committee contains exactly 2 republicans and at least 1 democrat.

The city of Raleigh has 10500 registered voters. There are two candidates for city council in...

The city of Raleigh has 10500 registered voters. There are two candidates for city council in an upcoming election: Brown and Feliz. The day before the election, a telephone poll of 600 randomly selected registered voters was conducted. 259 said they'd vote for Brown, 325 said they'd vote for Feliz, and 16 were undecided. Give the sample statistic for the proportion of voters surveyed who said they'd vote for Brown. Note: The proportion should be a fraction or decimal, not...