Question

learning goals from lesson 5.2
✓ i can find probabilities of independent and dependent event, and i can find conditional probabilities. (standards: s.cp.1, s.cp.2, s.cp.3, s.cp.5, s.cp.6, s.cp.8+)
lesson reflection (circle one)
starting... getting there... got it!
4.
a grab bag contains 2 football cards and 8 basketball cards. an experiment consists of taking one card out of the bag, replacing it, and then selecting another card. determine whether the events are independent. what is the probability of selecting a football card and then a basketball card? express your answer as a decimal.
a. not independent; 0.04
c. not independent; 0.64
b. independent; 0.16
d. independent; 0.18

Explanation:

Step1: Determine if events are independent

Since we replace the card after the first draw, the outcome of the first draw does not affect the second draw. So the events (drawing a football card first and a basketball card second) are independent.

Step2: Calculate probability of football card

Total cards = \(2 + 8 = 10\). Probability of football card (\(P(F)\)) = \(\frac{2}{10} = 0.2\).

Step3: Calculate probability of basketball card

Probability of basketball card (\(P(B)\)) = \(\frac{8}{10} = 0.8\).

Step4: Calculate combined probability

For independent events, \(P(F \text{ and } B) = P(F) \times P(B)\). So \(0.2 \times 0.8 = 0.16\).

Answer:

b. independent; 0.16