Tree Diagrams & Combined Probability Practice Questions

Amara plants two sunflower seeds.

The probability that a sunflower seed germinates is $0.8$.

The probability tree diagram shows some of this information.

A bag contains $5$ red counters and $3$ blue counters.

Oliver takes at random a counter from the bag and writes down its colour.
He puts the counter back in the bag.
He then takes at random a second counter from the bag and writes down its colour.

There are $7$ pens in a pencil case.
$4$ of the pens are blue and $3$ of the pens are red.

Suki takes at random a pen from the pencil case and keeps it.
She then takes at random a second pen from the pencil case.

Nadia takes two shots at a target with a bow and arrow.

Each time she shoots, the probability that she hits the target is $0.7$.
The result of her second shot is independent of the result of her first shot.

A machine seals bags of crisps.
Some of the bags are not sealed properly. These bags are faulty.

On each of three days, a worker checks a sample of bags from the machine.
The table shows the results.

The machine is going to seal two more bags of crisps.

A box contains $10$ sweets.
$4$ of the sweets are mints and $6$ of the sweets are toffees.

Mia takes at random a sweet from the box and eats it.
She then takes at random a second sweet from the box.

Jake says,

"The probability that Mia takes two mints is $\frac{4}{10} \times \frac{4}{10} = \frac{4}{25}$"