Two groups of climbers (team A and Team B) attempt to climb Mount everest using different routes. The probability of Team A reaching the summit is .70, The probability of Team B reaching the summit is .85.
A. Sue calculated the probability the both teams reach the top in the following manner: P(team A reaches the top and Team B reaches the top)=(.70)(.85)=0.595
In finding the probability, Sue assumed that the two events are:
i. Independant ii Dependant iii Mutually exclusiveiv Not Mutually Exclusive
B. assuming that Sue was correct in part a, what is the probability that Team A OR team B reaches the top?
b.) .955
A. Sue assumed that the two events are independent. In an independent event, the outcome of one event does not affect the probability or outcome of the other event. So, in this case, Sue multiplied the probabilities of Team A reaching the top (.70) and Team B reaching the top (.85) because she assumed that the success of each team is not dependent on the success or failure of the other.
B. Assuming Sue was correct in part A, to find the probability that Team A OR Team B reaches the top, we need to calculate the probability of at least one of the events happening.
To do this, we can find the probability of the complement of both events not happening and then subtract it from 1.
The complement of both events not happening is the probability that neither Team A nor Team B reaches the top. This can be calculated by subtracting the probability of both events happening (0.595) from 1.
So, the probability of neither reaching the top is 1 - 0.595 = 0.405.
Therefore, the probability of Team A OR Team B reaching the top is 1 - probability of neither team reaching the top. Hence, it is 1 - 0.405 = 0.595.