Question

Given R and T are two mutually exclusive events of an experiment with P(R)=0.49 and P(T)=0.09, caiculate the following probabilities. (o) P(Rᶜ ) =

(b) P(7C) =
(c) P(R∩T) =
(d) P(R∪T) =
(e) P(R∩Dᶜ =
(i) P(Rᶜ UTᶜ ) =

Answer 1

To calculate the given probabilities, we can use the formula: (a) P(Rᶜ) = 1 - P(R) = 1 - 0.49 = 0.51 (b) P(R∩T) = 0, because R and T are mutually exclusive (c) P(R∪T) = P(R) + P(T) = 0.49 + 0.09 = 0.58 (d) P(R∩Dᶜ) = P(R) - P(R∩D) = P(R) - P(R), because R and D are also mutually exclusive. Therefore, P(R∩D) = 0. (e) P(Rᶜ UTᶜ) = P(Rᶜ) + P(Tᶜ) = P(R) + P(T) = 0.49 + 0.09 = 0.58

Step-by-step explanation:

To calculate the given probabilities, we can use the formula:

(a) P(Rᶜ ) = 1 - P(R) = 1 - 0.49 = 0.51

(b) P(R∩T) = 0, because R and T are mutually exclusive (meaning they cannot occur at the same time).

(c) P(R∪T) = P(R) + P(T) = 0.49 + 0.09 = 0.58

(d) P(R∩Dᶜ) = P(R) - P(R∩D) = P(R) - P(R), because R and D are also mutually exclusive. Therefore, P(R∩D) = 0.

(e) P(Rᶜ UTᶜ) = P(Rᶜ) + P(Tᶜ) = P(R) + P(T) = 0.49 + 0.09 = 0.58