A space station has 5 cosmonauts on board at all times, of whom 3 are experienced, 2 inexperienced. Occasionally some work must be done outside the space station. The probability of being selected to carry out the work is twice as large for each individual experienced cosmonaut as it is for each inexperienced cosmonaut. Experienced cosmonauts have a 10% chance of getting into difficulties whilst outside, inexperienced cosmonauts 25%. (i) Calculate the probability that the cosmonaut selected is an experienced one.

Question

A space station has 5 cosmonauts on board at all times, of whom 3 are experienced, 2 inexperienced. Occasionally some work must be done outside the space station. The probability of being selected to carry out the work is twice as large for each individual experienced cosmonaut as it is for each inexperienced cosmonaut. Experienced cosmonauts have a 10% chance of getting into difficulties whilst outside, inexperienced cosmonauts 25%. (i) Calculate the probability that the cosmonaut selected is an experienced one.

Answer 1

To calculate the probability that the cosmonaut selected is an experienced one, we need to consider the number of experienced and inexperienced cosmonauts on board and the selection process.

Given that the space station has 5 cosmonauts, and 3 of them are experienced while 2 are inexperienced, the total number of cosmonauts can be represented as:
Total cosmonauts = Experienced cosmonauts + Inexperienced cosmonauts
Total cosmonauts = 3 + 2
Total cosmonauts = 5

Now, we need to determine the probability of selecting an experienced cosmonaut.

Let's consider the relative probabilities of selection for experienced and inexperienced cosmonauts. It is mentioned that the probability of being selected for experienced cosmonauts is twice as large as for inexperienced cosmonauts.

Let's denote the probability of selection for inexperienced cosmonauts as "x" (since it is not explicitly given).

According to the information provided, the probability of selection for experienced cosmonauts is twice that of inexperienced cosmonauts, which means it is 2x.

To find the value of "x", we can set up an equation using the given probabilities.
x + 2x = 1 (Since the sum of probabilities must be equal to 1)

Combining the terms on the left side of the equation:
3x = 1

Dividing both sides by 3:
x = 1/3

So, the probability of selecting an inexperienced cosmonaut is 1/3, and the probability of selecting an experienced cosmonaut is 2/3.

Hence, the probability that the cosmonaut selected is an experienced one is 2/3 or approximately 0.667.