Difficulty with Discrete probability? (1 Viewer)

[starbuckscoffee]

1. Find the probability that, in three tosses of a fair coin, there are three heads, given that there is at least one head.

2. The chance that a harvest is poorer than average is .5, but if it is known that a certain disease is present, this probabilty increases to .8. The disease B is present in 30% of the harvest. Find the probabilty hat, when the harvest is observed to be poorer than average, the disease is present.

3. A bag contains three red, four white and five black balls. If three balls are taken without replacement, what is the probability that they are all the same colour?

 

[lolokay]

1. 1/8 chance of no heads - so 7 ways of getting at least 1 head
1 way of getting 3 heads, so a 1/7 probability

2. 70% is not diseased, so .5*70% = 35/100 will be poorer than average but not diseased
30% is diseased, so .8*30% = 24/100 will be poorer than average and diseased
so if a harvest is poorer than average, there is a (24/100)/(24/100+35/100) = 24/59 probability that it the disease is present.

3. total of 12 balls
P(3 red) = 3/12*2/11*1/12 = 6/1728
P(3 white) = 4/12*3/12*2/12 = 24/1728
P(3 black) = 5/12*4/12*3/12 = 60/1728
Total = 90/1728 = 5/96