Question

RStudio / Combinations / Probability

-------------------------------------------------

Question

---

a) A pizza shop offers a ‘create your own pizza’ option, where customers can choose the toppings to go on the tomato base of the pizza. There are 6 different pizza toppings, and customers choose 2 of the 6 toppings to be included on the pizza.

i) How many different choices of two toppings are possible?

ii) One of the six possible toppings is olive. Jack wants to choose a pizza without olive. How many different choices of two toppings are possible when olive is not to be included?

---

b) You are given three events C, D and E with probabilities P(C)=0.4, P(D)=0.8 and P(E)=0.2.

It is known that P(C or D)=0.88,  P(C or E)=0.6 and P(D or E)=0.35

i) Select the pair of mutually exclusive events. (C, E or C, D or D,E?)

ii) Select the pair of independent events. (C,D or D,E or C,E?)

---

Please show methods/working

Answer 1

a)

i)

Different possible choices of two toppings that are possible=

ii)Exluding olive topings their a total of 5 topings to be chosen from.

Different possible choices of two toppings that are possible, when olive is not included=

b)

i)

A pair of events are mutually exclusive if there intersection is .

Hence , C and E are mutually exclusive

ii)

From the calculation done in i) we conclude that only for C and D, we have , hence C and D are independent.