P(R or S)=.64 P(R)=.38 P(S)=.52
Probability Union Rule
P(R and S)=P(R)+P(S)-P(R and S)
.64=.38+.52-P(R and S)
.54=.9-P(R and S)
At this point, how do I deal with the
-P(R and S)? I know the final answer is .26, but how do I get there?
treat P(R and S) as a variable, suppose it is x, then your first equation becomes
P(R or S) = P(R) + P(S) - x , .... you have a typo here
.64 = .38 + .52 - x
x = .9 - .64
x = .26
P(R and S) = .26
Thanks
To find the value of -P(R and S), we need to rearrange the equation:
0.54 = 0.9 - P(R and S)
Now, let's isolate P(R and S) by subtracting 0.9 from both sides:
0.54 - 0.9 = -P(R and S)
Simplifying the left side of the equation:
-0.36 = -P(R and S)
To get the value of P(R and S), we can simply multiply both sides of the equation by -1:
0.36 = P(R and S)
Therefore, the probability of the intersection of events R and S is 0.36.
Since we know that P(R or S) is 0.64 and we have already found the value of P(R and S), we can use the formula for the probability of the union to find the value of P(R or S):
P(R or S) = P(R) + P(S) - P(R and S)
= 0.38 + 0.52 - 0.36
= 0.9
Hence, the final answer is 0.9.