Probability Trees - Dependent Events - Miss B's Resources

Download PDF
10 downloads 390 Views 530KB Size Report
Comment
There is a tin of 10 biscuits in the maths office. Inside the tin there are 3 Digestive Biscuits and 7. Hobnobs. Andrea
Probability Trees - Dependent Events There is a tin of 10 biscuits in the maths office. Inside the tin there are 3 Digestive Biscuits and 7 Hobnobs. Andrea takes two biscuits at random from the tin to eat. Complete the probability tree diagram.

1st

Choice

2nd Choice Digestive

There are 4 black pens, 4 blue pens and 2 red pens in a pack.

There are 𝑛 chocolates in a bag. 4 of the chocolates are mint chocolate and the rest are plain chocolate.

Maria takes at random a pen from the pack notes the colour and gives it to a student.

a) Work out the probability of selecting a mint chocolate.

Work out the probability she selects two pens the same colour.

b) Work out the probability of selecting a plain chocolate.

Digestive Hobnob

c) Calculate the probability of randomly selecting two mint chocolates from the bag to eat.

Digestive Hobnob Hobnob

Work out the probability the two biscuits were not the same type.

www.missbsresources.com

Answers Probability Trees - Dependent Events There is a tin of 10 biscuits in the maths office. Inside the tin there are 3 Digestive Biscuits and 7 Hobnobs. Andrea takes two biscuits at random from the tin to eat. Complete the probability tree diagram. 1st Choice

3 10

Digestive

2 9 7 9

2nd Choice Digestive

Hobnob

3 Digestive 9 Hobnob 6 Hobnob 9 Work out the probability the two biscuits were not the 3 7 21 same type. 𝑃 𝐷, 𝐻 = Γ— = 10 9 90 21 21 7 3 21 𝑃 π‘π‘œπ‘‘ π‘†π‘Žπ‘šπ‘’ = + 90 90 𝑃 𝐻, 𝐷 = 10 Γ— 9 = 90 42 7 = = 90 15 7 10

There are 4 black pens, 4 blue pens and 2 red pens in a pack.

There are 𝑛 chocolates in a bag. 4 of the chocolates are mint chocolate and the rest are plain chocolate.

Maria takes at random a pen from the pack notes the colour and gives it to a student.

a) Work out the probability of selecting a mint chocolate. 4 𝑃 𝑀𝑖𝑛𝑑 = 𝑛

Work out the probability she selects two pens the same colour.

𝑃 π΅π‘™π‘Žπ‘π‘˜, π΅π‘™π‘Žπ‘π‘˜ = 𝑃 𝐡𝑙𝑒𝑒, 𝐡𝑙𝑒𝑒 = 𝑃 𝑅𝑒𝑑, 𝑅𝑒𝑑 =

4 3 12 Γ— = 10 9 90

4 3 12 Γ— = 10 9 90

2 1 2 Γ— = 10 9 90

𝑃 π‘†π‘Žπ‘šπ‘’ πΆπ‘œπ‘™π‘œπ‘’π‘Ÿ = =

b) Work out the probability of selecting a plain chocolate. π‘›βˆ’4 𝑃 π‘ƒπ‘™π‘Žπ‘–π‘› = 𝑛 c) Calculate the probability of randomly selecting two mint chocolates from the bag to eat. 𝑃 𝑀, 𝑀 =

12 12 2 + + 90 90 90

=

16 8 = 90 45

=

www.missbsresources.com

4 3 Γ— 𝑛 π‘›βˆ’1 12 𝑛 π‘›βˆ’1 12 βˆ’π‘›

𝑛2