Probability of independent events?
Please help me with this probability question:
Suppose that A and B are independent events such that P(Ā) = 0.1 and P(B) = 0.4
Find P(A ∩ B) and P(A U B)
- Randy PLv 71 decade agoFavorite Answer
Since P(Ā) = 0.1, P(A) = 0.9.
P(A ∩ B) = P(A) * P(B). That is the definition of independent events. So just multiply the two probabilities together.
P(A U B) is a little more complicated. It is equal to P(A) + P(B) for mutually exclusive events that can't both occur, but for independent events, they can both occur (with a probability calculated above).
The general expression is:
P(A U B) = P(A) + P(B) - P(A ∩ B)
so just use the value of P(A ∩ B) you calculated above.
- hickieLv 43 years ago
Flipping a coin and the replace in gasoline fees are not precisely the comparable ingredient. on a similar time as the two aspects of the coin are the two probable to be shown after a turn. Predicting gasoline fees has similarities to predicting the aspects. that is not any longer thoroughly random. For an occasion, in case you experienced sunny days all week, that is very no longer likely that it will rain day after immediately. that is termed conditional possibility. via fact the events are no longer self sustaining you need to subject upon handed events. that is similar to gasoline fees. they do no longer look to be in basic terms self sustaining of each and every little thing else. these days gasoline fees are extremely intense and the possibility that they are going to be low the next day are rather low.
- 1 decade ago
P(A n B)=P(A) x P(B) = 0.1 x 0.4 = 0.04
P(A U B)= P(A) + P(B) = 0.1+0.4=0.5