Math Is Fun Forum

Identity

Member

Registered: 2007-04-18

Posts: 934

Conditional Probability

The chance that a harvest is poorer than average is 0.5, but if it is known that a certain disease D is present, this probability increases to 0.8. The disease D is present in 30% of the harvests. Find the probability that, when the harvest is observed to be poorer than average, the disease D is present.

Cycling to school each morning, a girl goes through three sets of traffic lights. The probability of stopping at the first set is 0.6. If she stops at any one set, the probability that she has to stop at the next is 0.9. If she doesn't have to stop at any one set, the probability that she doesn't have to stop at the next is 0.7. Find the probability that
a) She has to stop at all three lights
b) She stops only at the second set of lights
c) She stops at exactly one set of lights

Thankyou!

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Conditional Probability

For the first one, split it up into cases and find the probability for each case.  Remember that the probability for a case only occurs when the assumptions are met.  How often (percentage-wise) are those assumptions met?

For the second, it's a bit more involved and if you're really struggling after solving the first, a decision tree is probably a good idea.

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Conditional Probability

Are the answers

0.48

a) 0.486
b) 0.028
c) 0.13?