Questions: f. The probability of A or B can always be found by just adding together the probability of A and the probability True False g. To find an "and" probability, you will need to multiply together the probabilities of each individual event True False h. If you are dealt one card from a 52 -card deck, then the probability that you are dealt an ace is 1/52. True False P(B A) is the probability that event B occurs given that the sample space is restricted to the outcomes associated True False j. If you roll a 6 -sided die one time, then the probability that you roll a 2 or a 3 is 1/6 * 1/6=1/36. True False

f. The probability of A or B can always be found by just adding together the probability of A and the probability
True
False
g. To find an "and" probability, you will need to multiply together the probabilities of each individual event
True
False
h. If you are dealt one card from a 52 -card deck, then the probability that you are dealt an ace is 1/52.
True
False
P(B A) is the probability that event B occurs given that the sample space is restricted to the outcomes associated
True
False
j. If you roll a 6 -sided die one time, then the probability that you roll a 2 or a 3 is 1/6 * 1/6=1/36.
True
False

Transcript text: f. The probability of A or B can always be found by just adding together the probability of A and the probability True False g. To find an "and" probability, you will need to multiply together the probabilities of each individual event True False h. If you are dealt one card from a 52 -card deck, then the probability that you are dealt an ace is $\frac{1}{52}$. True False $\mathrm{P}(\mathrm{B} \mid \mathrm{A})$ is the probability that event B occurs given that the sample space is restricted to the outcomes associated True False j. If you roll a 6 -sided die one time, then the probability that you roll a 2 or a 3 is $\frac{1}{6} \cdot \frac{1}{6}=\frac{1}{36}$. True False

Solution

Solution Steps

Solution Approach

f. The probability of A or B can be found by adding the probabilities of A and B only if A and B are mutually exclusive events. Otherwise, you must subtract the probability of both A and B occurring together.

g. To find an "and" probability for independent events, you multiply the probabilities of each individual event.

h. The probability of being dealt an ace from a 52-card deck is the number of aces divided by the total number of cards, which is 4/52 or 1/13.

Step 1: Probability of A or B

To find the probability of either event A or event B occurring, we use the formula: \[ P(A \cup B) = P(A) + P(B) - P(A \cap B) \] Substituting the values: \[ P(A) = 0.3, \quad P(B) = 0.4, \quad P(A \cap B) = 0.1 \] Thus, \[ P(A \cup B) = 0.3 + 0.4 - 0.1 = 0.6 \]

Step 2: Probability of A and B

To find the probability of both events A and B occurring together, we use the formula for independent events: \[ P(A \cap B) = P(A) \cdot P(B) \] Substituting the values: \[ P(A) = 0.3, \quad P(B) = 0.4 \] Thus, \[ P(A \cap B) = 0.3 \cdot 0.4 = 0.12 \]

Step 3: Probability of Being Dealt an Ace

The probability of being dealt an ace from a standard 52-card deck is given by: \[ P(\text{Ace}) = \frac{\text{Number of Aces}}{\text{Total Cards}} = \frac{4}{52} = \frac{1}{13} \approx 0.0769 \]