Question

Two customers A and B are visiting a particular shop in the same week (Monday to Friday). Each of them is equally likely to visit the shop on any of these days. The probability that both will visit the shop on consecutive days is:

[1 mark]

• A. $\frac{4}{25}$
• B. $\frac{8}{25}$
• C. $\frac{12}{25}$
• D. $\frac{16}{25}$

Answer 1

The correct option is B $\frac{8}{25}$

A and B can visit the shop on Monday, Tuesday, Wednesday, Thursday, and Friday.

Let M = Monday, T = Tuesday, W = Wednesday, Th = Thursday, F = Friday

Then, the total possible outcomes are:
(M, M), (M, T), (M, W), (M, Th), (M, F)
(T, M), (T, T), (T, W), (T, Th), (T, F)
(W, M), (W, T), (W, W), (W, Th), (W, F)
(Th, M), (Th, T), (Th, W), (Th, Th),
(Th, F), (F, M), (F, T), (F, W), (F, Th),
(F, F)

Total possible outcomes = 25
A and B visit the shop on consecutive days.

Favourable outcomes = (M, T), (T, M), (T, W), (W, T), (W, Th), (Th, W), (Th, F), (F, Th) = 8 outcomes

$\therefore Probability=\frac{\text{Number of favourable outcomes}}{\text{Number of possible outcomes}}=\frac{8}{25}$