question\nharry has a bag containing 6 red balls and 4 yellow balls. sara has a bag containing 3 red balls…

question\nharry has a bag containing 6 red balls and 4 yellow balls. sara has a bag containing 3 red balls, 2 black balls, and 5 yellow balls.\nwhich statements describe a pair of independent events?\nselect all the correct answers.\n□ harry randomly selects a red ball from his bag, and sara randomly selects a red ball from her bag.\n□ harry randomly selects a yellow ball from his bag, replaces the ball in the bag, and then randomly selects another yellow ball from his bag.\n□ harry randomly selects a red ball from his bag and then selects a yellow ball from his bag without replacing the first ball.\n□ sara randomly selects a yellow ball from her bag, replaces the ball in the bag, and then randomly selects a red ball from her bag.\n□ harry randomly selects a yellow ball from his bag, and sara randomly selects a red ball from her bag.\n□ sarah randomly selects two yellow balls from her bag without replacement.

question\nharry has a bag containing 6 red balls and 4 yellow balls. sara has a bag containing 3 red balls, 2 black balls, and 5 yellow balls.\nwhich statements describe a pair of independent events?\nselect all the correct answers.\n□ harry randomly selects a red ball from his bag, and sara randomly selects a red ball from her bag.\n□ harry randomly selects a yellow ball from his bag, replaces the ball in the bag, and then randomly selects another yellow ball from his bag.\n□ harry randomly selects a red ball from his bag and then selects a yellow ball from his bag without replacing the first ball.\n□ sara randomly selects a yellow ball from her bag, replaces the ball in the bag, and then randomly selects a red ball from her bag.\n□ harry randomly selects a yellow ball from his bag, and sara randomly selects a red ball from her bag.\n□ sarah randomly selects two yellow balls from her bag without replacement.

Answer

Explanation:

Step1: Recall definition of independent events

Two events are independent if the occurrence of one does not affect the probability of the occurrence of the other.

Step2: Analyze each option

Option 1:

Harry's selection from his bag and Sara's selection from her bag are independent since they are different bags. The outcome of Harry's selection does not affect Sara's selection and vice - versa.

Option 2:

When Harry replaces the ball after the first selection, the probability of the second selection remains the same as the first. So the first and second selections are independent.

Option 3:

Since there is no replacement, the probability of the second selection (selecting a yellow ball) is affected by the first selection (selecting a red ball). So these are dependent events.

Option 4:

Since Sara replaces the ball, the probability of the second selection (selecting a red ball) is not affected by the first selection (selecting a yellow ball). So these are independent events.

Option 5:

Harry's selection from his bag and Sara's selection from her bag are independent as they are from different bags.

Option 6:

Without replacement, the probability of the second selection of a yellow ball is affected by the first selection of a yellow ball. So these are dependent events.

Answer:

Harry randomly selects a red ball from his bag, and Sara randomly selects a red ball from her bag. Harry randomly selects a yellow ball from his bag, replaces the ball in the bag, and then randomly selects another yellow ball from his bag. Sara randomly selects a yellow ball from her bag, replaces the ball in the bag, and then randomly selects a red ball from her bag. Harry randomly selects a yellow ball from his bag, and Sara randomly selects a red ball from her bag.