8. Probability of Compound Events
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The events are mutually exclusive.
The events are mutually exclusive.
The events are mutually exclusive.
The events are overlapping events.
4/5
3/5
1
4/5
Consider the following cards.
Given the cards, we are asked to find the probability of getting a number or the letter B if a card is chosen randomly. Since B is not a number, the events are mutually exclusive. If A and B are mutually exclusive events, P(AorB) is given as follows. P(Aor B)=P(A)+P(B) With this in mind, we first need to find the probability of P(B) and P(number). P(B)&= 1/5 [1em] P(number)&= 3/5
Finally, let's add these probabilities to get P(B or number). P(B or number)&= 1/5+ 3/5 &⇓ P(B or number)&=4/5Now, we are asked to find the probability of getting a red card or the number 5 if a card is chosen randomly. Since the number five is a yellow card, the events are mutually exclusive. Again, we first need to find P(red) and P(5).
Now, we are asked to find the probability of getting a red card or a yellow card if a card is chosen randomly. Since a card cannot be red and yellow at the same time, the events are mutually exclusive. Again, we first need to find P(red) and P(yellow).
Finally, we are asked to find the probability of getting a yellow card or a letter if a card is chosen randomly. Note that the card with the letter B is also yellow. Thereforewe have overlapping events. If A and B are overlapping events, P(A or B) is given as follows.
P(AorB)=& P(A)+P(B) [0.3em]
&-P(AandB)
Let's set A=yellow and B=letter. We can now rewrite the given formula as follows.