Compound events consist of two or more simple events that are connected by the words and or or. Let’s investigate a case where simple events are connected by the word and.
Choosing a counter from bag 1 did not affect choosing a
counter from bag 2. These events are called independent events because the outcome of one
event does not affect the outcome of the other event.
You can analyze the experiment with a tree diagram.
There are four equally-likely outcomes. So, the probability
of choosing white on the first draw and white on the second draw is ¼.
You can also multiply to find the probability of two independent events.
Example
1. Two dice are rolled. Find the probability that an odd number is rolled on
the first die and the number 4 is rolled on the second.
Alternative Solutions :
Two events can also be connected by the word or. For
example, consider the probability of drawing a jack or a queen from a standard deck
of 52 cards. Since a card cannot be both a jack and a queen, the events are mutually exclusive. That
is, both events cannot occur at the same time.
The probability of two mutually exclusive events is found by
adding.
The probability of drawing a jack or a queen is 123 .
Example
2. Jamal has 4 quarters, 2 dimes, and 4 nickels in his pocket. He takes one
coin from his pocket at random. What is the probability that the coin is either
a quarter or a dime?
Alternative Solutions :
A coin
cannot be both a quarter and a dime, so the events are mutually exclusive. Find
the sum of the individual probabilities.
Sometimes events are connected by the word or, but
they are not mutually exclusive. For example, suppose there is a chance of rain
on Saturday and there is a chance of rain on Sunday. You want to find the chance
of rain over the weekend. Because it could rain on both Saturday and Sunday,
rainfall on Saturday and Sunday are not mutually exclusive events. The two
events are called inclusive
events.
Example
Meteorology Link
3.
If
there is a 40% chance of rain on Saturday and a 60% chance of rain on Sunday,
find the probability that it will rain on either Saturday or Sunday.
Alternative Solutions :
Since it is possible to rain on both days, these events are inclusive.
P(Saturday) = 0.4 P(Sunday)
= 0.6
These events are independent since the weather on Saturday does not affect
the weather on Sunday.
P(Saturday or Sunday)
= P(Saturday) + P(Sunday)
– P(Saturday and Sunday)
= 0.4 + 0.6 (0.4) – (0.6)
= 1.0 – 0.24 Simplify.
= 0.76 or 76% Write as a
percent.
The probability that it will rain on the weekend is 76%.
Sumber
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