8. Probability of Compound Events
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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)&=4/5P(red)&= 2/5 [1em] P(5)&= 1/5 Finally, let's add this probabilities to get P(red or5). P(red or5)&= 2/5+ 1/5 &⇓ P(red or5)&=3/5
P(red)&= 3/5 [1em] P(yellow)&= 2/5 Finally, let's add this probabilities to get P(red or yellow). P(red or yellow)&= 3/5+ 2/5 &⇓ P(red or yellow)&=1
P(yellow or letter) = P(yellow) + P(letter) [0.5em] -P(yellow and letter) With this in mind, we first need to find the probability of P(yellow), P(letter), and P(yellow and letter). P(yellow)=& 3/5 [1em] P(letter)=& 2/5 [1em] P(yellow and letter)=& 1/5 Therefore, by substituting the above values into the rewritten equation, we can calculate P(yellow or letter). P(yellow or letter)&= 3/5+ 2/5- 1/5 &⇓ P(yellow or letter)&=4/5