gcse probability

What is probabilty?

Probability is the chance or likelihood that something will happen. All probabilities lie between th numbers from 0 to 1.

Exhaustive events account for all possible outcomes e.g

When 2 coins are tosed simultaneously the possible out comes are..

hh, tt, ht, th h=heads t=tails

Mutually exclusive events are events that cannot happen at the same time.

The probability of an event = Number of ways an event can happen/total number of outcomes.

Example: John has a bag of jelly babies. In his bag he has 5 red, 7 green and 6 yellow jely babies. John picks a jelly baby at random. What is the probability tat he will pick...

a) a red jelly baby

b) a yellow or red jelly baby

a) p=5/18 We got this answer as we know by adding the total no. of jelly babies in his bag together we get 18, and 5 out of this 18 are red so the probability that he will pick a red jelly baby is 5 out of 18 which is written as 5/18.

b) p (red or yellow) = 11/18

If two outcomes of an event are Mutually exclusive, then

p (outcome will happen) = 1-p (outcome will not happen)

Example 1

The probability that team GB will win the 2012 Olympics is 6/10. Whatis the probabilty that they will not win?

p(will not win) = 1-p(will win)

= 1 - 6/10

= 4/10

Example 2 - The probability that it will snow this Christmas is 0.67. What is the probability that it will not snow?

p(won't snow) = 1 - p(will snow)

= 1 - 0.67

= 0.33

Relative frequencies are used to estimate probability.

Relative frequency of an event = Number of times event occured/total no. of trials.

Example

when a fair die is thrown 40 times a 1 came up 12 times. What is the relative frequency of getting a 1.

no. of trials = 40

no. of ones = 12

relative frequency = 12/40 = 0.3

If a fair die is thrown 300 times approximatley how many twos are likely to be obtained. There are 6 possible outcomes and all are equally likely.

P(2) = 1/6 times 300 = 50 twos

Multiply 300 by 1/6 since a two is expected 1/6 of the time.

When two evets are independant the outcome of the second event is not affected by the outcome of the first. If two or more events are independent the probability of a and b and c happening together is p (a and b and c) = a times b times c

Example - The probablity that it will rain on any day in september is 4/10. Find the probability that: A) It will rain on both the 1st and 3rd of september

B) it will rain on the 10th of september but not the 20th

a) 4/10 times 4/10 = 16/100

b) 4/10 times 6/10 = 24/100