Question

Assume that in a particular military exercise involving two units, Red and Blue, thereis a 60 % chance that the Red unit will successfully meet its objectives and a 70% chance that the Blue unit will do so. There is an 18 % chance that only theRed unit will be successful. What is the probability that both units will meet theirobjectives? What is the probability that one or the other but not both of the unitswill be successful?

Answer 1

Answer: a) There are 42% chances that both units will meet their objectives.

b) There are 88% chances that one or the other but not both of the units will be successful.

Step-by-step explanation:

Since we have given that

Probability that the Red unit will successfully meet its objectives = 60% = P(R)

Probability that Blue unit will successfully meet its objectives = 70% = P(B)

Probability that only Red unit will be successful = P(only Red) = 18%

As we know that

$P(only\ red)=P(R)-P(R\cap B)\\\\0.18=0.60-P(R\cap B)\\\\0.18-0.60=-P(R\cap B)\\\\-0.42=-P(R\cap B)\\\\P(R\cap B)=42\%$

Hence, there are 42% chances that both units will meet their objectives.

the probability that one or the other but not both of the units will be successful is given by

$P(R\cup B)=P(R)+P(B)-P(R\cap B)\\\\P(R\cup B)=0.60+0.70-0.42\\\\P(R\cup B)=0.88\\\\P(R\cup B)=88\%$

Hence, there are 88% chances that one or the other but not both of the units will be successful.