more Probability problems

tronter

[tex] P(\text{stop at first light signal}) = 0.4 = P(A) [/tex]

[tex] P(\text{stop at second light signal}) = 0.5 = P(B) [/tex]

[tex] P(\text{stop at least one of two signals}) = 0.6 = P(A \cup B) [/tex]

Then [tex] P(A \cap B) = P(A) + P(B) - P(A \cup B) = 0.3 [/tex]

[tex] P( \text{first signal but not second}) = P(A \cap B') = 1-0.3 = 0.7 [/tex]

[tex] P(\text{exactly one signal}) = P(A \cup B) - P(A \cap B) = P(A \Delta B) = 0.3 [/tex]


Are these correct?

EnumaElish

They are; except can you explain P(1st but not 2nd) = 0.7?

tronter

yeah thats incorrect. It should be [tex] P(A \cap B') = P(A) - P(A \cap B) = 0.4-0.3 = 0.1 [/tex]

Jrb599

Shouldn't it be [tex]P(A \cap B') = P(A) * (1-P(B))[/tex]

Assuming there independent