Question

two coins are tossed and a spinner numbered from 1 to 8 is spun. what is the probability that both coins land heads up and the spinner lands on a number less than 3?
\\(\frac{1}{32})\
\\(\frac{1}{16})\
\\(\frac{1}{8})\
\\(\frac{1}{4})

Explanation:

Step1: Calculate probability of two - head coins

The probability of getting a head on one coin toss is $\frac{1}{2}$. Since the two coin - tosses are independent events, the probability of getting two heads is $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step2: Calculate probability of spinner landing on a number less than 3

The spinner has 8 possible outcomes (numbers 1 - 8). The numbers less than 3 are 1 and 2, so there are 2 favorable outcomes. The probability of the spinner landing on a number less than 3 is $\frac{2}{8}=\frac{1}{4}$.

Step3: Calculate the combined probability

Since the coin - tosses and the spinner spin are independent events, we multiply the probabilities of the two events. The combined probability is $\frac{1}{4}\times\frac{1}{4}=\frac{1}{16}$.

Answer:

$\frac{1}{16}$