Question

probability of independent and dependent events
this quiz will test your knowledge on independent and dependent events in probability.
value: 2
suppose a fair coin is tossed and a 6 - sided number cube is rolled. what is the probability that the coin lands on tails and the outcome on the number cube is a number less than 3?
a. 1/12
b. 1/6
c. 1/9
d. 1/3

Explanation:

Step1: Find probability of coin - tails

A fair coin has 2 possible outcomes (heads or tails). The probability of getting tails, $P(T)=\frac{1}{2}$.

Step2: Find probability of number - cube less than 3

A 6 - sided number cube has 6 possible outcomes. The numbers less than 3 are 1 and 2, so there are 2 favorable outcomes. The probability of getting a number less than 3, $P(N<3)=\frac{2}{6}=\frac{1}{3}$.

Step3: Use multiplication rule for independent events

Since the coin - toss and the number - cube roll are independent events, the probability of both events occurring is $P = P(T)\times P(N < 3)$. Substitute the values: $P=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$.

Answer:

B. 1/6