rule of thumb
If a bag contains 5 red balls, 3 green balls, and 2 blue balls, what is the probability of drawing a red or green ball?
Total balls = 5 (red) + 3 (green) + 2 (blue) = 10.
The probability is 0.8 (or 80%).
If event A has a probability of 0.4 and event B has a probability of 0.3, what is the probability of either A or B occurring if the events are mutually exclusive?
Since the events are mutually exclusive, the probability of either A or B occurring is simply the sum of the individual probabilities.
P(A∪B)=P(A)+P(B)=0.4+0.3=0.7P(A \cup B) = P(A) + P(B) = 0.4 + 0.3 = 0.7P(A∪B)=P(A)+P(B)=0.4+0.3=0.7
In a deck of 52 cards, what is the probability of drawing either a heart or a queen?
13/52+4/52-1/52
16/52
In a deck of 52 cards, what is the probability of drawing a queen, given that the card drawn is a face card?
The probability is 1/3 (or about 33.33%).
If the probability of event A is 0.5 and the probability of event B is 0.6, what is the probability that both A and B occur if the events are independent?
For independent events, the probability of both events occurring is the product of their individual probabilities.
P(A∩B)=P(A)×P(B)=0.5×0.6=0.3P(A \cap B) = P(A) \times P(B) = 0.5 \times 0.6 = 0.3P(A∩B)=P(A)×P(B)=0.5×0.6=0.3
If the probability of it raining tomorrow is 0.4 and the probability of you getting a cold is 0.2, what is the probability that both events happen if they are independent?
The probability is 0.08 (or 8%).
A die is rolled and a coin is flipped. What is the probability of rolling an even number on the die and getting heads on the coin?
The probability is 0.25 (or 25%).
Are the events "rolling a 3 on a die" and "rolling an even number on a die" mutually exclusive? Why or why not?
Yes, these events are mutually exclusive. A die cannot show both a 3 (which is odd) and an even number at the same time, so they cannot occur together.
What is the probability of drawing either a red or a yellow marble from a jar containing 4 red marbles, 3 yellow marbles, and 5 green marbles?
7/12
When calculating the probability of drawing two cards from a deck of 52 without replacement, how would you decide whether to use the addition or multiplication rule?
Use the addition rule for "either/or" events, and the multiplication rule for "both" events happening
If you draw a card from a standard deck and it is known that the card is a heart, what is the probability that it is the queen of hearts?
There are 13 hearts in a deck, and only one of them is the queen. The probability of drawing the queen of hearts given that you know the card is a heart is:
P(Queen of Hearts∣Heart)=113P(\text{Queen of Hearts} | \text{Heart}) = \frac{1}{13}P(Queen of Hearts∣Heart)=131
In a class of 20 students, 12 are boys and 8 are girls. If a student is known to be a girl, what is the probability that she has a pet, given that 4 girls in the class have a pet?
4/8 or 1/2