Maths Probabilty
posted by Kesha .
1. From a bag containing 5 gold and 3 red marbles that feel identical, one is drawn at random. If the first marble drawn is not replaced before the second is drawn:
i) Explain why the probability of picking the second gold marble is 4/7 and why the probability of picking two gold marbles = 5/8 x 4/7.
ii) List all possibilities and their probabilities.
iii) If the experiment was repeated 560 times, how many times would you expect to get:
A) two gold marbles?
B) different coloured marbles?
2. A pencil case has 12 identically shaped coloured pencils in it. 3 are yellow, 4 are red and 5 are green. You pick two pencils one after another at random. (not replacing first, then picking another)
i) Explain why the probability of picking the second yellow pencil is 2/11, and why the probability of picking two yellow pencils is 3/12 x 2/11.
ii)What two coloured pencils are you most likely to pick?
iii) What two coloured pencils are you least likely to pick?
Explain your reasoning for both.
c) If 4 pencils are picked one after another at random, which of the following groups :
YRRG YYGG GGGG YRRR
do you expect to be:
i) more likely to be picked?
ii) least likely to be picked?
d) Work out the probability of each group above, and compare it with your expectations.
3. Caroline chooses a marble from a bag. Describe the possbile contents of this bag if the probability of her choosing :
a) a green marble is 1/8
b) a green marble is 1/8 the first time she chooses a marble, but 1/15 the second time, if the green marble was not put back or replaced after she picked it out the first time.
c) a green marble is 1/8 the first time she chooses a marble, but 3/31 the second time, if the green marble was not put back or replaced after she picked it out the first time.
4 a) Describe the possible contents of a bag if when Malcolm chooses a marble from the bag, the probability of him choosing a purple marble is 1/3.
b) If malcolm returns the purple marble to the bag in a), then chooses another marble, discuss what is the probability that the second marble is also purple.
c) If Malcolm keeps the purple marble in a) then chooses another, discuss what is the probability that the second marble is also purple.
d) If Malcolm chooses a marble from the bag, the probability of him choosing a black marble is 2/3 while the probability of him choosing a purple marble is 1/3. describe the posible contents of the bag.
THANK YOU VERY MUCH

We do not do your homework for you. However, I will give you a start.
i) The probability of picking a first gold marble is 5/8, since there are 5 gold marbles among the eight total. If you do not replace it, 4 gold marbles are among the remaining 7.
The probability of two or more events all occurring is found by multiplying the probabilities of the individual events.
I hope this helps.