A space vehicle is designed to land on Mars. Assume that the ground condition on Mars is either hard or soft. If hard ground is encountered during landing, the vehicle will be successfully landed with probability 0.9, whereas, if soft ground is encountered, the corresponding probability of a successful landing is only 0.5. Based on the available information, it is judged that the chance of hitting hard ground is three times that of hitting soft ground. a. What is the probability of a successful landing? b. Suppose a stick can be projected to test the ground condition before landing. It will penetrate into soft ground with probability 0.9, and hard ground with probability of only 0.2. If the stick were observed to penetrate into the ground, what is the probability that the ground is hard? c. What is the probability of a successful landing if the stick penetrated the ground?
A space vehicle is designed to land on Mars. Assume that the ground condition on Mars is either hard or soft. If hard ground is encountered during landing, the vehicle will be successfully landed with
a. What is the probability of a successful landing?
b. Suppose a stick can be projected to test the ground condition before landing. It will penetrate into soft ground with probability 0.9, and hard ground with probability of only 0.2. If the stick were observed to penetrate into the ground, what is the probability that the ground is hard?
c. What is the probability of a successful landing if the stick penetrated the ground?
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