Question

Let B and C be two events such that P (B) = 0.24 and P (C) = 0.33.Do not round your responses.(a) Determine P (BUC), given that B and C are mutually exclusive.Dilbevewri(b) Determine P (BUC), given that B and C are independent.nTampin to 25m S bijud of show CSS 96

Answer 1

Given:

Let B and C be two events such that P (B) = 0.24 and P (C) = 0.33.

Required:

(a) Determine P (BUC), given that B and C are mutually exclusive.

(b) Determine P (BUC), given that B and C are independent.

Step-by-step explanation:

The concept required:

a). For mutually exclusive events, the probability of both the events occurring at the same time is equal to zero.

`\begin{gathered} P(B\cup C)=P(B)+P(C) \\ =0.24+0.33 \\ =0.57 \end{gathered}`

b).For independent events, the probability of both the events occurring at the same time is equal to non zero.

So,

`\begin{gathered} P(B\cap C)=P(B)* P(C) \\ =0.24*0.33 \\ =0.0792 \end{gathered}`

and

`\begin{gathered} P(B\cup C)=P(B)+P(C)-P(B\cap C) \\ =0.24+0.33-0.0792 \\ =0.4908 \end{gathered}`

Answer:

Determined the values of P (BUC) for both cases.