Probability of independent events Practice Questions

Warm-upeasy

A fair coin is flipped twice. What is the probability of getting heads on both flips?

Each flip has a probability of $1$ out of $2\textsf{,}$ or $\dfrac{1}{2}\textsf{.}$ The flips are independent, so $\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}\textsf{.}$

Mid-gameeasy

A standard six-sided die is rolled twice. What is the probability of rolling a $6$ on both rolls?

Each roll has a probability of $1$ out of $6\textsf{,}$ or $\dfrac{1}{6}\textsf{.}$ The rolls are independent, so $\dfrac{1}{6} \times \dfrac{1}{6} = \dfrac{1}{36}\textsf{.}$

Mid-gameeasy

A standard six-sided die is rolled, then a fair coin is flipped. What is the probability of rolling an even number and then getting heads?

Rolling an even number has a probability of $3$ out of $6\textsf{,}$ or $\dfrac{1}{2}\textsf{.}$ Heads has a probability of $1$ out of $2\textsf{,}$ or $\dfrac{1}{2}\textsf{.}$ The events are independent, so $\dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{4}\textsf{.}$

Mid-gameeasy

A spinner has $4$ equal sections and exactly $1$ is red. You spin it once and flip a fair coin. What is the probability of landing on red and getting heads?

Red has a probability of $1$ out of $4\textsf{,}$ or $\dfrac{1}{4}\textsf{.}$ Heads has a probability of $1$ out of $2\textsf{,}$ or $\dfrac{1}{2}\textsf{.}$ The events are independent, so $\dfrac{1}{4} \times \dfrac{1}{2} = \dfrac{1}{8}\textsf{.}$

Mid-gameeasy

A bag holds $2$ red marbles and $3$ blue marbles. You draw one marble, put it back, and draw again. What is the probability that both draws are red?

Each draw has a probability of $2$ out of $5\textsf{,}$ or $\dfrac{2}{5}\textsf{.}$ The marble is replaced, so the draws are independent: $\dfrac{2}{5} \times \dfrac{2}{5} = \dfrac{4}{25}\textsf{.}$

Mid-gameeasy

A standard six-sided die is rolled twice. What is the probability that both rolls are greater than $4\textsf{?}$

The faces greater than $4$ are $5$ and $6\textsf{,}$ so each roll has a probability of $2$ out of $6\textsf{,}$ or $\dfrac{1}{3}\textsf{.}$ The rolls are independent, so $\dfrac{1}{3} \times \dfrac{1}{3} = \dfrac{1}{9}\textsf{.}$

Mid-gameeasy

A fair coin is flipped $3$ times. What is the probability of getting heads all $3$ times?

Each flip has a probability of $1$ out of $2\textsf{,}$ or $\dfrac{1}{2}\textsf{.}$ The flips are independent, so $\dfrac{1}{2} \times \dfrac{1}{2} \times \dfrac{1}{2} = \dfrac{1}{8}\textsf{.}$

Buzzer beatereasy

A spinner has $5$ equal sections and exactly $1$ is blue. You spin it twice. What is the probability it lands on blue both times?

Each spin has a probability of $1$ out of $5\textsf{,}$ or $\dfrac{1}{5}\textsf{.}$ The spins are independent, so $\dfrac{1}{5} \times \dfrac{1}{5} = \dfrac{1}{25}\textsf{.}$

Probability of independent events. Game on.

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