Use the Venn Diagram to illustrate the following situation.
Mario has 45 red chips, 12 blue chips and 24 white chips. Illustrate the probability that Mario randomly selects a red chip or a white chip.
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Use the Venn Diagram to illustrate the following situation.
Mario has 45 red chips, 12 blue chips and 24 white chips. Illustrate the probability that Mario randomly selects a red chip or a white chip.
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Answer:
2723
Step-by-step explanation:
Answer:
\frac{23}{27}2723
Step-by-step explanation:
Probabilities that deal with multiple events are called compound events. These events can occur at the same time, called mutually inclusive or not occur at the same time, called mutually exclusive.
Some events that might happen at the same time are drawing a face card from a standard deck of 52 cards, or drawing a heart. Drawing the king of hearts satisfies both events. This means that drawing a face card and drawing a heart are mutually inclusive events.
The probability of 2 compound events, A and B, is given by the formula
P (A \ or\ B) = P(A) + P(B) - P(A \ and\ B)P(A or B)=P(A)+P(B)−P(A and B)
where
P (A or B) is the probability that A or B occurs.
P(A) is the probability of A occurring.
P(B) is the probability of B occurring.
P(A and B ) is the probability that A and B occur at the same time.
We need to subtract the instance when the two events happen to avoid at the same time to avoid double counting. In our example, drawing a king of hearts is also drawing a face card or drawing a heart; counting it again would result in double counting.
If two events are mutually exclusive, or cannot happen at the same time, P(A and B) is 0.
For our problem, we count first our possible outcomes. We have 45 red chips, 12 blue chips and 24 red chips. We add all of them together
45+12+24=8145+12+24=81
There are 81 possible outcomes.
Drawing a red chip or a white chip cannot happen at the same time. These events are mutually exclusive.
Therefore, we can just add the probability of drawing a red chip to the probability of drawing a white chip.
\begin{gathered}P(red \ or \ white) = P(red)+P(white)+P(red \ and \ white)\\\\P(red \ or \ white) = \frac{45}{81}+\frac{24}{81}+0\\\\P(red \ or \ white) = \frac{69}{81}\\\\P(red \ or \ white) = \frac{3*23}{3*27}\\\\P(red \ or \ white) = \frac{23}{27}\\\end{gathered}P(red or white)=P(red)+P(white)+P(red and white)P(red or white)=8145+8124+0P(red or white)=8169P(red or white)=3∗273∗23P(red or white)=2723
The probability of drawing a red chip or a white chip is \frac{23}{27}.
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