Question

The probabilities that two students will not show up for class on a beautiful spring day are 0.3 and 0.4, respectively. It is a beautiful spring day. Find the following probabilities. (See Example 6. Round your answers to two decimal places.) (a) Neither will show up for class. (b) Both will show up for class. (c) Exactly one will show up for class.

Answer 1

(a) 0.12

(b) 0.42

(c) 0.46

Explanation:

Probability of student A not showing up = 0.3

Probability of student B not showing up = 0.4

(a) Neither will show up for class

`P(A\ and\ B) = 0.3*0.4 = 0.12`

(b) Both will show up for class

`P (A\ nor\ B) = (1-0.3)*(1-0.4) = 0.42`

(c) Exactly one will show up for class

`P(A\ or\ B) = 1 -P(A\ and\ B) - P(A\ nor\ B)\\P(A\ or\ B) = 1 -0.12-0.42 = 0.46`