# Probability

﻿I DO KNOW MR.PITT HAS ALREADY DONE A PROBABILITY PAGE!

Probability is demonstrated with a fraction, for example:
There are 10 marbles in a bag, 5 are black, 2 are white, 1 is each blue and red.
What is the probability of picking a black marble at random?
Answer: Obviously $\inline \frac{1}{2}$

Now a harder question:

What is the probability of choosing a black marble, putting it back, then choosing a red?

Answer: You would do $\inline \frac{1}{2} X \frac{1}{10}$, which makes $\inline \frac{1}{20}$

Even Harder:

What is the probability of choosing a black without putting it back, and then choosing a blue?

Answer: Do $\inline \frac{1}{2} X \frac{1}{9} = \frac{1}{18}$

Tree Diagrams:

FIRST

A tree diagram of a coin being tossed 3 times looks like this:
 image: tree diagram and probabilities

The probability of three heads is:
P (H H H) = 1/2 × 1/2 × 1/2 = 1/8
P (2 Heads and a Tail) = P (H H T) + P (H T H) + P (T H H)
= 1/2 × 1/2 × 1/2 + 1/2 × 1/2 × 1/2 + 1/2 × 1/2 × 1/2
= 1/8 + 1/8 + 1/8
= 3/8

Question:
 image: tree diagram with missing probabilities

Fill in the missing probabilites