Assume that Jim Bruce Valerie is Simeon are four of 33 members of the class and that four of the class members will be chosen randomly to deliver their reports during the next class meeting what is the probability that Jim Bruce Valerie and salmon are selected in that order use decimal four and the decimals had to be rounded to the sixth Place.
To find the probability of Jim, Bruce, Valerie, and Simeon being selected in that order, we need to calculate the probability of each individual being selected, considering that the choices are made without replacement.
The probability of Jim being selected first is 1/33, since there are 33 members total and we are selecting one at a time.
The probability of Bruce being selected second is 1/32, as there are 32 members remaining after Jim has been selected.
The probability of Valerie being selected third is 1/31, since there are 31 members remaining after Jim and Bruce have been selected.
The probability of Simeon being selected fourth is 1/30, as there are 30 members remaining after Jim, Bruce, and Valerie have been selected.
To calculate the overall probability, we multiply these individual probabilities:
P(Jim, Bruce, Valerie, Simeon) = (1/33) * (1/32) * (1/31) * (1/30)
Rounding this value to the sixth decimal place, we get:
P(Jim, Bruce, Valerie, Simeon) ≈ 0.000003
To find the probability of Jim, Bruce, Valerie, and Simeon being selected in that specific order, we need to calculate the probability of each event happening one after the other.
Since there are 33 members in the class and 4 of them will be chosen, the probability of Jim being selected first is 1/33.
After Jim is selected, there are 32 members left and we need to calculate the probability of Bruce being selected second. The probability of Bruce being chosen is 1/32.
Similarly, after Jim and Bruce are selected, there are now 31 members left and we need to calculate the probability of Valerie being selected third. The probability of Valerie being chosen is 1/31.
Lastly, after Jim, Bruce, and Valerie are selected, there are 30 members left, and the probability of Simeon being chosen fourth is 1/30.
To find the probability of all these events happening together, we multiply the probabilities:
(1/33) * (1/32) * (1/31) * (1/30) = 0.0000005134
Rounding this value to the sixth decimal place, the probability that Jim, Bruce, Valerie, and Simeon are selected in that order is approximately 0.000001.