Grade 11 probability mayh

Question

You have a bag of marbles that contains 5 red, 2 white and 7 blue.

a) what are the ODDS of picking a red AND blue marble.

b) what are the ODDS of picking two marbles that are different colours

c) what is the PROBABILITY of picking a red and a blue marble

d) what is the PROBABILITY of picking two marbles that are different colours

Answer 1

Probability first....

Sampling with replacement:

Prob( RED and BLUE) = 5/14 * 7/14 = 5/26

Prob( different colors) = 1 - Prob( same color)

= 1 - 5/14*5/14 - 2/14*2/14 - 7/14*7/14

= 1 - 25/196 - 1/49 - 1/4

= (196 - 25 - 4 - 49)/196

= 117/196

Odds of RED and BLue: 5 to 19

Odds of 2 different colors : 117 to 82

Sampling without replacement:

Prob(RED and Blue) =

(5*2)/(14*13) = 10/182 = 5/91,

which is 5 to 86 odds

1 - Prob( same color) =

1 - (5*4)/182 - (2*1)/182 - (7*6)/182

( 182 - 20 - 2 - 42)/182

118/182 = 59/91 , which is 59 to 32 odds

Generally speaking, if the probability is a/b

then the odds are a to (a-b)