Maths4U Original · Short practice

Two independent signals A and B occur with probabilities \(\displaystyle \frac{3}{5}\) and \(\displaystyle \frac{2}{5}\). In a separate sequence, \(\displaystyle r=4\) independent trials each have success probability \(\displaystyle \frac{3}{5}\).

Find P(A and B).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent signals A and B occur with probabilities \(\displaystyle \frac{1}{5}\) and \(\displaystyle \frac{1}{2}\). In a separate sequence, \(\displaystyle r=5\) independent trials each have success probability \(\displaystyle \frac{1}{5}\).

Find P(A and B).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent signals A and B occur with probabilities \(\displaystyle \frac{1}{5}\) and \(\displaystyle \frac{1}{2}\). In a separate sequence, \(\displaystyle r=5\) independent trials each have success probability \(\displaystyle \frac{1}{5}\).

Find P(exactly one of A and B).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent signals A and B occur with probabilities \(\displaystyle \frac{3}{10}\) and \(\displaystyle \frac{3}{5}\). In a separate sequence, \(\displaystyle r=6\) independent trials each have success probability \(\displaystyle \frac{3}{10}\).

Find P(exactly one of A and B).

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent signals A and B occur with probabilities \(\displaystyle \frac{3}{10}\) and \(\displaystyle \frac{3}{5}\). In a separate sequence, \(\displaystyle r=6\) independent trials each have success probability \(\displaystyle \frac{3}{10}\).

Find the probability of at least one success in the r trials.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent signals A and B occur with probabilities \(\displaystyle \frac{2}{5}\) and \(\displaystyle \frac{3}{10}\). In a separate sequence, \(\displaystyle r=3\) independent trials each have success probability \(\displaystyle \frac{2}{5}\).

Find the probability of at least one success in the r trials.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent signals A and B occur with probabilities \(\displaystyle \frac{2}{5}\) and \(\displaystyle \frac{3}{10}\). In a separate sequence, \(\displaystyle r=3\) independent trials each have success probability \(\displaystyle \frac{2}{5}\).

Find the probability that all r trials succeed.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.

Maths4U Original · Short practice

Two independent signals A and B occur with probabilities \(\displaystyle \frac{1}{2}\) and \(\displaystyle \frac{2}{5}\). In a separate sequence, \(\displaystyle r=4\) independent trials each have success probability \(\displaystyle \frac{1}{2}\).

Find the probability that all r trials succeed.

Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.