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

0.3023

Step-by-step explanation:

86 band members

26 are senior, 17 plays trumpet. If 4 are seniors and play trumpet, we solve this using the bayes theorem of conditional probability.

Probability of choosing band member that plays trumpet =17/86 = 2/43.

Probability of choosing a senior that plays trumpet = 4/26

Probability that a chosen member is a senior given that he plays trumpet = (2/43)/(4/26)

= 0.3023.

85.560%

step-by-step explanation:

conditional probability is defined as:

p(a|b) = p(a∩b) / p(b)

in other words, the probability that a occurs, given that b has occurred = the probability that both a and b occur / the probability that b occurs.

in this example:

p(turns 64 | turns 44) = p(turns 64 & turns 44) / p(turns 44).

if someone turns 64, they must have already turned 44, so:

p(turns 64 | turns 44) = p(turns 64) / p(turns 44)

on page 42, we see that of the original 100,000, 94944 turn 44, and 81234 turn 64.   therefore:

p(turns 64 | turns 44) = 81234 / 94944

p(turns 64 | turns 44) = 0.85560