Suppose that a high school marching band has 86 members. Of these 86 band members, 26 are seniors, 17 play the trumpet, and 4 are seniors who play the trumpet. What is the probability that a randomly selected band member is a senior given that he or she plays the trumpet? Give your answer as a percentage, rounded to one decimal place. What is the probability that a randomly selected band member plays the trumpet given that he or she is a senior?

a) 0.4117 = 41.2% to 1 d.p

b) 0.2693 = 26.9% to 1 d.p

Step-by-step explanation:

Total number of members of the marching band = n(U) = 86

Number of seniors in the marching band = n(S) = 26

Number of trumpet players in the marching band = n(T) = 17

Number of seniors who are trumpet players in the marching band = n(S n T) = 4

Probability that a randomly selected member of the marching band is a senior = P(S) = (26/86) = 0.3023

Probability that a randomly selected member of the marching band is a trumpet player = P(T) = (17/86) = 0.1977

Probability that a randomly selected member of the marching band is a senior and a trumpet player = P(S n T) = (7/86) = 0.0814

a) The probability that a randomly selected band member is a senior given that he or she plays the trumpet is the conditional probability, P(S|T)

Mathematically. It is given as

P(S|T) = P(S n T)/P(T)

P(S|T) = (0.0814/0.1977)

P(S|T) = 0.4117 = 41.2% to 1 d.p

b) The probability that a randomly selected band member plays the trumpet given that he or she is a senior = P(T|S)

P(T|S) = P(S n T)/P(S)

P(T|S) = (0.0814/0.3023)

P(T|S) = 0.2693 = 26.9%

Hope this Helps!!!

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."