Verify that the given function f(x)=6e−6x over [0,∞) satisfies the property that the area under the curve is 1. Compute the antiderivative F(x)=−e6x1 and evaluate the limit limb→∞[F(b)−F(0)] to show the area is 1.
Flights from Dallas to Chicago are on time 80% of the time. 20 flights are randomly selected. Find the probability of exactly 12 on-time flights, fewer than 12 on-time flights, at least 12 on-time flights, and between 10 and 12 on-time flights. Interpret the probabilities.
A. Probability that none of the 32 people are Independent: (1−0.12)32 B. Probability that fewer than 6 are Independent: ∑i=05(i32)(0.12)i(1−0.12)32−i C. Probability that more than 3 people are Independent: 1−∑i=03(i32)(0.12)i(1−0.12)32−i
Spin two game board spinners, one with 1,2,3 and one with 5,6,7,8. The first spinner's digit is the tens, the second's is the ones. Construct a tree diagram to show all possible prize amounts.
Bag of 33 tulip bulbs: 14 red, 11 yellow, 8 purple. Select 2 bulbs randomly without replacement. Find probabilities: (a) both red, (b) first red, second yellow, (c) first yellow, second red, (d) one red, one yellow. (a) Probability both bulbs are red: 3314⋅3213
(b) Probability first bulb is red, second is yellow: 3314⋅3211
(c) Probability first bulb is yellow, second is red: 3311⋅3214
(d) Probability one bulb is red, one is yellow: (3314⋅3211)+(3311⋅3214)