Questions: Suppose P(B)=0.5, P(D)=0.4. Find the probability below. a. P(D^c) a. P(D^c)= (Type an exact answer in simplified form.)

Transcript text: Suppose $P(B)=0.5, P(D)=0.4$. Find the probability below. a. $P\left(D^{c}\right)$ a. $P\left(D^{c}\right)=$ $\square$ (Type an exact answer in simplified form.)

Solution

Solution Steps

Step 1: Understand the complement rule

The complement of an event $ D $, denoted as $ D^c $, represents all outcomes that are not in $ D $. The probability of the complement of an event is given by: \[ P(D^c) = 1 - P(D) \]

Step 2: Substitute the given probability

Given $ P(D) = 0.4 $, substitute this value into the complement rule: \[ P(D^c) = 1 - 0.4 \]

Step 3: Calculate the result

Perform the subtraction to find $ P(D^c) $: \[ P(D^c) = 0.6 \]