# Find the smallest possible value of P(A and B)

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#1
Q: http://prntscr.com/xmzsml

If A and B are mutually exclusive then they cannot happen together, so the smallest possible value would be 0 or else it would be (0.9 x 0.7) = 0.63. However, in the textbook it says 0.6...
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1 year ago
#2
(Original post by TSR360)
Q: http://prntscr.com/xmzsml

If A and B are mutually exclusive then they cannot happen together, so the smallest possible value would be 0 or elswe it would be (0.9 x 0.7) = 0.63. However, in the textbook it says 0.6...
What do they sum to? What are the laws of probability?
Independence is an important property for probability functions, but the intersection can be less or more than that value. It's not a bound. In a Venn diagram, the sets can overlap anything between 0 and min(A,B).
Last edited by mqb2766; 1 year ago
1
1 year ago
#3
(Original post by TSR360)
Q: http://prntscr.com/xmzsml

If A and B are mutually exclusive then they cannot happen together, so the smallest possible value would be 0 or else it would be (0.9 x 0.7) = 0.63. However, in the textbook it says 0.6...
It might help you to remember the rule P(A u B) = P(A) + P(B) - P(A n B) (you can see this from a Venn diagram).

Remember that P(A u B) is a probability, so that its max value is 1. What does that tell you about P(A n B)?
1
1 year ago
#4
The probability that A happens is 0.9 and that B happens is 0.7. The minimum possible probability is (1-0.9) + (1-0.7) which would get the value of 0.4, 1-0.4 = 0.6
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