Probability Question 204
Question: A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and $ A\cap B= $ card is ace of diamond, then events A and B are
Options:
A) Independent
B) Mutually exclusive
C) Dependent
D) Equally likely
Show Answer
Answer:
Correct Answer: C
Solution:
It is obvious.
Event A is that the card is a diamond. There are 13 diamonds in a deck of 52 cards.
Event B is that the card is an ace. There are 4 aces in a deck of 52 cards.
The intersection of A and B, denoted as $A∩B$ , is the event that the card is an ace of diamonds.
There is 1 ace of diamonds in a deck of 52 cards.
If we know that event A has occurred (i.e., the card drawn is a diamond), it changes the probability that event B will occur (i.e., the card drawn is an ace).
This is because within the diamonds, only one card is an ace. So, the occurrence of event A affects the probability of event B, and vice versa. Hence, events A and B are dependent.
BETA
