Answer:
Example:
A bag contains 3 black balls and 5 white balls. Paul picks a ball at random from the bag and replaces it back in the bag. He mixes the balls in the bag and then picks another ball at random from the bag.
a) Construct a probability tree of the problem.
b) Calculate the probability that Paul picks:
i) two black balls
ii) a black ball in his second draw
Solution:
tree diagram
a) Check that the probabilities in the last column add up to 1.
b) i) To find the probability of getting two black balls, first locate the B branch and then follow the second B branch. Since these are independent events we can multiply the probability of each branch.
ii) There are two outcomes where the second ball can be black.
Either (B, B) or (W, B)
From the probability tree diagram, we get:
P(second ball black)
= P(B, B) or P(W, B)
= P(B, B) + P(W, B)
NOT MY WORDS TAKEN FROM A SOURCE!
(x^2) <64 => (x^2) -64 < 64-64 => (x^2) - 64 < 0 64= 8^2 so (x^2) - (8^2) < 0 To solve the inequality we first find the roots (values of x that make (x^2) - (8^2) = 0 ) Note that if we can express (x^2) - (y^2) as (x-y)* (x+y) You can work backwards and verify this is true. so let's set (x^2) - (8^2) equal to zero to find the roots: (x^2) - (8^2) = 0 => (x-8)*(x+8) = 0 if x-8 = 0 => x=8 and if x+8 = 0 => x=-8 So x= +/-8 are the roots of x^2) - (8^2)Now you need to pick any x values less than -8 (the smaller root) , one x value between -8 and +8 (the two roots), and one x value greater than 8 (the greater root) and see if the sign is positive or negative. 1) Let's pick -10 (which is smaller than -8). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0 so it is positive
2) Let's pick 0 (which is greater than -8, larger than 8). If x=0, then (x^2) - (8^2) = 0-64 = -64 <0 so it is negative3) Let's pick +10 (which is greater than 10). If x=-10, then (x^2) - (8^2) = 100-64 = 36>0 so it is positive Since we are interested in (x^2) - 64 < 0, then x should be between -8 and positive 8. So -8<x<8 Note: If you choose any number outside this range for x, and square it it will be greater than 64 and so it is not valid.
Hope this helped!
:)
Hector = 2s or h/2
Sister = s
Equation: h/2 = s
Substitution: (20)/2 = s
10 = s
Hector’s sister found 10 seashells.
20% of $720( original cost)= $144 (discount)
$720- $ 144 = $576 (discounted cost)
5% tax = $36 (tax payed)
tax + cost of phone = $612 (total of both tax and discounted cost)
20% of $612=$122.40 (deposit cost?)
