Question

what is the probability of having two different outcomes on the coins and spinning an odd number?
\\(\frac{1}{16}\\)
\\(\frac{1}{8}\\)
\\(\frac{1}{4}\\)
\\(\frac{1}{2}\\)

Explanation:

Step1: Calculate coin - outcome probability

When flipping two coins, the total number of outcomes is $2\times2 = 4$ (HH, HT, TH, TT). The number of outcomes with two different results is 2 (HT and TH). So the probability of getting two different outcomes on two coins, $P_{coin}=\frac{2}{4}=\frac{1}{2}$.

Step2: Calculate spinner - outcome probability

The spinner has 4 sections numbered 1 - 4. The odd - numbered sections are 1 and 3. So the number of favorable outcomes is 2, and the total number of outcomes is 4. The probability of spinning an odd number, $P_{spinner}=\frac{2}{4}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since the coin - flipping and spinner - spinning are independent events, the probability of both events occurring is the product of their individual probabilities. $P = P_{coin}\times P_{spinner}$. Substitute $P_{coin}=\frac{1}{2}$ and $P_{spinner}=\frac{1}{2}$ into the formula, we get $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Answer:

$\frac{1}{4}$