Can someone please help me. A single card is selected from a standard 52-card deck. B= the drawn card is black; R= the drawn card is red; Q= the drawn card is a queen; F= the drawn card is a face card ( a king, queen or jack). Without finding the probabilities, determine if B and R are independent, without finding probabilities, determine if B and Q are independent, without finding the probabilities, determine if F and Q are independent. Using the probabilities, determine if B and R are independent. Using the probabilities determine if B and Q are independent. Using the probabilities, determine if F and Q are independent.
To determine whether two events are independent, we need to compare the probabilities of the events occurring individually to the probability of both events occurring together. If the probabilities are the same, the events are independent; otherwise, they are dependent.
Without finding probabilities:
1. Are B and R independent?
- We know that black cards and red cards are mutually exclusive (i.e., a card cannot be both black and red), so B and R are dependent events. If a card is black, it cannot be red, and vice versa.
2. Are B and Q independent?
- Since a queen can be either black or red, there is a possibility for B and Q to be independent. However, without more information, we cannot definitively determine the answer. We would need to find the probabilities to assess independence.
3. Are F and Q independent?
- Face cards (king, queen, and jack) may or may not include queens, so F and Q are dependent events. The presence of a queen affects the probability of the event "face card" occurring.
Using probabilities:
To determine independence using probabilities, we need to calculate the individual probabilities of each event and the probability of both events occurring together.
1. B and R independence:
- Calculate the probability of drawing a black card (B) and the probability of drawing a red card (R) separately.
- Calculate the probability of both a black card and a red card being drawn (B and R).
- If P(B) * P(R) = P(B and R), the events are independent. Otherwise, they are dependent.
2. B and Q independence:
- Calculate the probability of drawing a black card (B) and the probability of drawing a queen (Q) separately.
- Calculate the probability of both a black card and a queen being drawn (B and Q).
- If P(B) * P(Q) = P(B and Q), the events are independent. Otherwise, they are dependent.
3. F and Q independence:
- Calculate the probability of drawing a face card (F) and the probability of drawing a queen (Q) separately.
- Calculate the probability of both a face card and a queen being drawn (F and Q).
- If P(F) * P(Q) = P(F and Q), the events are independent. Otherwise, they are dependent.