also which are independent events?
a) a student spins a spinner. on the first spin she spins a six and on the second spin she spins a three
b) a student chooses a card from a deck of 20 cards. the student keeps the card and chooses another one.
c) a student tosses a coin three times. the results are heads,heads and tails
d) a student chooses a blue marble from a cup. the student returns it and chooses another marble.
i put a, b, and d is that correct?
Two of those answers are right.
which ones?
Yes, you are correct! Events A, B, and D are independent events.
To determine if events are independent, you need to check if the outcome of one event affects the outcome of the other event.
a) In this case, the student spins the spinner twice. The outcome of the first spin, a six, does not affect the outcome of the second spin, a three. Therefore, events A (spinning a six) and B (spinning a three) are independent.
b) The student chooses a card from a deck of 20 cards and keeps it. Then they choose another card from the remaining cards. The outcome of the first selection does not influence the outcome of the second selection. So, events A (choosing a card) and B (choosing another card) are independent.
c) The student tosses a coin three times and gets heads, heads, and tails. In this case, the outcome of each toss is independent of the others. The result of the first two tosses (heads) doesn't impact the outcome of the third toss (tails). Therefore, events A (getting heads on the first toss), B (getting heads on the second toss), and C (getting tails on the third toss) are independent.
d) The student chooses a blue marble from a cup, returns it, and then chooses another marble. The act of returning the first marble ensures that it may be chosen again. Hence, the outcome of the first selection does not affect the outcome of the second selection. Thus, events A (choosing a blue marble) and B (choosing another marble) are independent.
So, you correctly identified that events A, B, and D are the independent events in this scenario.