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)&=4/5
b Now, 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).
P(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
c 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).
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
d 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.
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
