probability and counting

posted by .

(1 pt) A box contains 25 yellow, 28 green and 38 red jelly beans.
If 13 jelly beans are selected at random, what is the probability that:
a) 5 are yellow?
b) 5 are yellow and 7 are green?
c) At least one is yellow?

  • probability and counting -

    In total, there are 25+28+38=91 jelly beans.

    Using (n,r) to stand for "n choose r"
    =n!/(r!(n-r)!)

    To choose y yellow, g green and r red jelly beans, the number of ways to choose is given by
    (25,y)*(28,g)*(38,r)
    and the number of ways to choose the same number of jelly beans irrespective of colour is
    (25+28+38,y+g+r)=(91,y+g+r)

    So the probability is:
    (25,y)*(28,g)*(38,r) / (91,y+g+r)

    For 5 yellow, we not worry about the other two colours, so they can be combined, call it x. We need 8 of x.
    Probability
    =(25,5)*(66,8)/(91,13)
    =53130*5743572120/1917283000904460
    =0.1592 (approx.)

    For (b), it is a similar expression. I get approx. 0.0012

    For (c), you would choose 13 out of green and red, and subtract from the probability of 1.
    1-(66,13)(25,0)/(91,13)
    =1-0.01
    =0.99 (approximately)

    See also following link for a detailed explanation:
    http://mathforum.org/library/drmath/view/69151.html

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    danielle has 30 jelly beans and 18 green jelly beans. What is the ratio of yellow jelly beans to greens jelly beans
  2. math

    The ratio of red jelly beans to yellow jelly beans in a dish is 2:3. If I eat 3 red jelly beans and 6 yellow ones the ratos is 4:5. How many yellow jelly beans were orginally in the dish?
  3. Math

    The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. if greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4;5. how many jelly beans were originally in the dish?
  4. Math

    The ratio of red jelly beans to yellow jelly beans in a dish is 3:4. If Greg eats 3 red jelly beans and 6 yellow ones, the ratio is 4:5. How many yellow jelly beans were originally in the dish?
  5. Math

    Tory has 4 blue jelly beans, 6 red jelly beans, 5 yellow jelly beans, and 1 green jelly bean in his bag. What fraction of the jelly beans are A)Blue B)Yellow C)Red D)Green
  6. math

    A jar of jelly beans contains 50 red gumballs , 45 yellow gumballs, and 30 green gumballs. You reach into the jar and randomly select a jelly bean, then select another without putting the first jelly bean back. What is the probability …
  7. Math

    You have a jar with 60 jelly beans. You know that 1/3 of the jelly beans are yellow, 1/4 of them are white and the rest is red. You are not allowed to look. How many beans do you have to take out to be absolutely sure to get at least …
  8. data management gr.12

    In a bag there are 8 red jelly beans and 7 green jelly beans. The 4 jelly beans are randomly chosen from the bag without replacement. a)create a probability distribution table for choosing red jelly beans b)what is the probability …
  9. math

    In a bag there are 8 red jelly beans and 7 green jelly beans. The 4 jelly beans are randomly chosen from the bag without replacement. a)create a probability distribution table for choosing red jelly beans b)what is the probability …
  10. data management gr.12

    In a bag there are 8 red jelly beans and 7 green jelly beans. The 4 jelly beans are randomly chosen from the bag without replacement. a)create a probability distribution table for choosing red jelly beans b)what is the probability …

More Similar Questions