Two companies are in danger of failing.𝑃(𝑀 fails),𝑃(𝐻 fails), and 𝑃(𝑀 and 𝐻 both fail) . the probability that 𝑀 fails and 𝐻 survives

probabilitystatistical-inferencestatistics

this is a probability question from a Master's course. The scenario is:

Two companies 𝑀 and 𝐻 are in danger of failing, analysts reckon that in the next year: 𝑃(𝑀 fails)=0.7, 𝑃(𝐻 fails)=0.6 and 𝑃(𝑀 and 𝐻 both fail)=0.5 .

  1. What is the probability that 𝑀 fails and 𝐻 survives?
  2. What is the probability that both will survive?

My thoughts so far are:

1-0.5 = 0.5, but that is unlikely to be correct.

Probability that at least one will fail is 0.7+0.6−(0.5)(0.7), but I still do not seem to get the correct answer.

Any help is appreciated.

Best Answer

Do a Venn's diagram and solve it immediatelyenter image description here

  1. 0.2

  2. try by yourself using the above diagram.

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