Combined & Conditional Probability Practice Questions

Work out the probability that both sets of lights are on red when Rosa reaches them.

Work out the probability that neither set of lights is on red when Rosa reaches them.

One of the 100 students is chosen at random.

Write down the probability that this student usually travels to school by car.

One of the Year 11 students is chosen at random.

Write down the probability that this student usually walks to school.

One of the 100 students is chosen at random.

Given that this student usually travels to school by bus, find the probability that the student is in Year 10.

Explain why Ravi's method may not give the correct probability.

5 of the 30 students have both a dog and a cat.

One of the 30 students is chosen at random.

Work out the probability that this student has a dog or has a cat.

Work out the probability that the two chocolates are the same type.

You must show your working.

Before doing any working, Jon said,

"5 out of the 12 chocolates are milk chocolates, so the probability that both chocolates are milk chocolates is $\frac{5}{12}\times\frac{5}{12}$"

Explain why Jon is wrong.

One of the 40 students is chosen at random.

Write down the probability that this student uses neither Netflix nor Spotify.

One of the 40 students is chosen at random.

Given that this student uses Spotify, find the probability that the student also uses Netflix.

Two of the 40 students are chosen at random.

Work out the probability that both of these students use neither Netflix nor Spotify.

Work out the probability that all three marbles are blue.

Work out the probability that at least one of the three marbles is white.

A bag contains only red counters and blue counters.

There are 6 red counters in the bag.

Sam takes at random two counters from the bag. He does not replace them.

The probability that both counters are red is $\frac13$

Work out the number of blue counters in the bag.

One of the 180 employees is chosen at random.

Work out the probability that this employee cycles to work.

One of the 180 employees is chosen at random.

Given that this employee cycles to work, find the probability that the employee is part-time.

A bag contains 12 beads.

3 of the beads are red, 4 of the beads are blue and 5 of the beads are green.

Maya takes at random three beads from the bag.

Work out the probability that she takes one bead of each colour.

You must show your working.

A switch is chosen at random from all the switches made by the factory.

Work out the probability that this switch is faulty.

A switch is chosen at random from all the switches made by the factory.

Given that this switch is faulty, find the probability that it was made on machine B.