Balls in a bag, probability involving selections etc.

In summary, the conversation includes a request for help with a friend's depression and stress, as well as questions about probability and fallacies in arguments. The conversation also includes a reminder to post individual problems and show attempts at solutions for assistance.
  • #1
ineedhelp2
1
0
HELP PLEASE! My friend is suffering huge depression and stress and she really needs to hand in this assignment or she will fail... please if you can answer any of these questions!

A bag contains x pink balls and y yellow balls. Three balls are randomly selected from the bag.

a) Write down an expression for the probability that the three balls chosen were pink.If there had been one more pink ball, then the probability that the three balls chosen were pink would have been double the answer found in a).
Show that y = (x^(2 )- x-2)/(5-x) .

Sketch a graph of x against y, and determine all the possible numbers of pink and yellow balls.

In a mixed class, there are 10 girls.
If 2 pupils are selected at random, the probability that they are both girls is 0.15
How many boys are in the class?
Three boxes are labelled A, B and C.
A contains 3 cubes, 4 pyramids and 5 spheres.
B contains 2 cubes, 1 pyramid and 7 spheres.
C contains 4 cubes, 5 pyramids and 6 spheres.
A shape is taken at random from each of the three boxes. Find the probability of
a) 3 cubes
b) a pyramid from A, a sphere from B and a pyramid from C
c) two pyramids and a sphere
d) no spheres
e) at least one sphere and no pyramids
f) no cubes or spheres
g) 3 cubes or 3 spheres
h) Either a cube or a sphere from A, a pyramid from B and either a cube or a pyramid from Ca) If 3 people are asked on which day of the week they were born, find the probability that
i) 2 or 3 are the same
ii) only 2 people are the same

b) If 4 people are asked the same question, find the probability that 2 or more were born on the same day.Comment on the following arguments, identifying precisely any fallacies in the arguments.

On every day of the year, it either rains or it doesn’t. Therefore the chance that it will rain tomorrow is 1/2.
When answering a multiple- choice test in which there are four possible answers given to each question, the chance that Gemma answers a question correctly is 1/4.
A bag contains a number of red, blue and white beads. If you choose one bead at random from the bag, the probability that it is blue is 1/3 .
Make up two “myths” of your own.
 
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  • #2
Re: Urgent help please

Hello and welcome to MHB! :) I'm very sorry for your friend. :( However, it is not our policy to solve lists of exercises for others. We believe everyone benefits most from a discussion, and we're all willing to guide you to a greater understanding and the answers. To do that, it would be best if you created separate threads for each problem and posted your attempts at solutions. :D We will be happy to put you in the right track then.

Cheers, and hope for the best.
 
  • #3
Re: Urgent help please

Along the same lines as Fantini said, pick one problem and show an attempt at it. Also, we won't give help with problems that are graded if the person's teacher/professor isn't ok with you getting help.

I'm sorry your friend is having issues with depression and we will be glad to help him or her understand math better, but we need you to do it on our terms which will actually benefit your friend the most in the future. :)

Long story short - pick one problem, show some work and convince us that we aren't helping you cheat.

Jameson
 

1. What is the probability of selecting a red ball from a bag containing 10 red balls and 20 blue balls?

The probability of selecting a red ball from a bag containing 10 red balls and 20 blue balls is 10/30 or 1/3. This is because there are 10 red balls out of a total of 30 balls in the bag.

2. If I randomly select 3 balls from a bag containing 12 red balls and 8 blue balls, what is the probability that all 3 balls will be red?

The probability of selecting 3 red balls from a bag containing 12 red balls and 8 blue balls is (12/20) * (11/19) * (10/18) = 0.229. This is because the probability of selecting a red ball on the first draw is 12/20, on the second draw it is 11/19, and on the third draw it is 10/18. These probabilities are multiplied together to get the overall probability of selecting 3 red balls in a row.

3. What is the probability of selecting 2 blue balls and 1 red ball from a bag containing 5 red balls and 10 blue balls?

The probability of selecting 2 blue balls and 1 red ball from a bag containing 5 red balls and 10 blue balls is (10/15) * (9/14) * (5/13) = 0.172. This is because the probability of selecting a blue ball on the first draw is 10/15, on the second draw it is 9/14, and on the third draw it is 5/13. These probabilities are multiplied together to get the overall probability of selecting 2 blue balls and 1 red ball in that specific order.

4. If I have a bag containing 8 green balls, 5 yellow balls, and 7 red balls, what is the probability of selecting a yellow ball on the first draw and a red ball on the second draw without replacing the first ball?

The probability of selecting a yellow ball on the first draw and a red ball on the second draw without replacing the first ball is (5/20) * (7/19) = 0.092. This is because the probability of selecting a yellow ball on the first draw is 5/20, and since we do not replace the first ball, the probability of selecting a red ball on the second draw is 7/19. These probabilities are multiplied together to get the overall probability of selecting a yellow ball and then a red ball without replacement.

5. If I have a bag containing 60 balls, 20 of which are black and 40 of which are white, what is the minimum number of balls I need to select to have a 50% chance of selecting at least one black ball?

The minimum number of balls needed to be selected to have a 50% chance of selecting at least one black ball is 26. This can be calculated using the formula 1 - (40/60)^n = 0.5, where n is the number of balls being selected. Solving for n, we get 26 as the minimum number of balls needed to be selected for a 50% chance of selecting at least one black ball.

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