of the physics graduates of a university, 35% received a starting salary of $50,000 or more. If 5 of the graduates are selected at random, find the probability that all had a starting salary of $50,000 or more.
Assume that there is an infinite number (or a large number) of physics graduates so that selecting 5 has negligible effect on the pool, then the proportion of well-paid graduates remains at 35%.
Then the probability for selecting one well-paid graduate is 0.35, and selecting 5 is 0.35^5=0.0053
To find the probability that all 5 selected graduates had a starting salary of $50,000 or more, we can use the concept of independent events.
Given that 35% of the physics graduates received a starting salary of $50,000 or more, this implies that the probability of any one graduate having a starting salary of $50,000 or more is 0.35.
Since the selection of each graduate is independent, the probability of all 5 selected graduates having a starting salary of $50,000 or more can be calculated by multiplying the probability of each individual event.
Therefore, the probability of each selected graduate having a starting salary of $50,000 or more is 0.35. Since there are 5 graduates being selected, we can multiply this probability by itself five times:
Probability of all 5 graduates having a starting salary of $50,000 or more = (0.35) * (0.35) * (0.35) * (0.35) * (0.35) ≈ 0.01358
So, the probability that all 5 selected graduates had a starting salary of $50,000 or more is approximately 0.01358 (or 1.36%).