There are 6 purple balls, 5 blue balls, and 3 green balls in a
box. 5 balls were randomly chosen (without replacing them). Find
the probability that
(a) Exactly 3 blue balls were chosen.
(b) 2 purple balls, 1 blue ball, and 2 green balls were
chosen.
A box contains 8 red balls, 4 green balls, and 3 blue balls. You
pull 2 balls from the box (one at a time) WITHOUT
replacement.
**LEAVE ALL ANSWERS AS FRACTIONS**
Find the probability of the following:
a.) P(Red on 1st ball AND Red on 2nd ball) =
b.) P(Green on 1st ball AND Red on 2nd ball)
=
c.) P(Blue on 1st ball AND Green on 2nd ball)
=
d.) What is the probability of drawing 2 green
balls...
Box A contains 6 red balls and 3 green balls, whereas box B
contains 3 red ball and 15 green balls.
Stage one. One box is selected at random in such a way that box
A is selected with probability 1/5 and box B is selected with
probability 4/5.
Stage two. Finally, suppose that two balls are selected at
random with replacement from the box selected at stage one.
g) What is the probability that both balls are red?
h)...
Box 1 contains 3 red balls, 5 green balls and 2 white balls. Box
2 contains 5 red balls, 3 green balls and 1 white ball. One ball of
unknown color is transferred from Box 1 to Box 2. (a) What is the
probability that a ball drawn at random from Box 2 is green? (b)
What is the probability that a ball drawn from Box 1 is not
white?
3. Box A contains 6 red balls and 3 green balls, whereas box B
contains 3 red ball and 15 green balls.
Stage one:One box is selected at random in such
a way that box A is selected with probability 1/5 and box B is
selected with probability 4/5.
Stage two: First, suppose that 1 ball is
selected at random from the box selected at stage one.
a) What is the probability that the ball is red?
b) Given that...
There are three types of balls in a box: 5 red, 3 blue and 2
green. You draw 3 balls at once (without replacement) from this box
and record: Y1=the # of red balls, Y2=the # of blue balls that you
drew. Find the joint probability distribution of Y1, Y2, by first
writing the possible values for y1, y2 in rows and columns and then
filling in the probabilities within this table. Then check that the
sum of the entries...
A box contains 100 Christmas light bulbs -- 40 green, 35 red and
25 blue. You randomly select two bulbs from the box with
replacement. The outcome of interest is the colour of each of the
two selected light bulbs. (a) List the complete sample space of
outcomes. (1 mark) (b) What is the probability that the two
selected bulbs are the same colour? (1 mark) (c) What is the
probability that the first selected bulb is green or that...
A box contains 4 red balls, 3 yellow balls, and 3 green balls.
You will reach into the box and blindly select a ball, take it out,
and then place it to one side. You will then repeat the experiment,
without putting the first ball back. Calculate the probability that
the two balls you selected include a yellow one and a green
one.
3. Consider a binomially distributed random variable constructed
from a series of 8 trials with a 60%...
An urn contains colored balls;5 red balls, 8 green balls, and 10
blue balls. Suppose If the 3 balls are drawn one after another
without replacement, what is the probability that the colors
observed will be Red, Green, Blue in this order? If the three
balls are drawn simultaneously from the urn (without replacement),
what is the probability that the selected balls will be all
different?
A box contains 100 balls, of which 15% are green, 40% are red,
and 45% are spotted.
Use simulation to find the probability that if you
randomly draw a ball you get a Red Ball.
Use the following 20 randomly generated numbers: 97, 52,
61, 87, 07, 48, 73, 49,
23, 75, 18, 15, 70, 34, 67, 40, 48, 98, 49,
70