a group of 350 people includes 187 play the flute, 172 play the clarinet, and 47 both the flute and the clarinet. a person is selected at random. 1. what is the probability that he/she plays the clarinet but not the flute? a. 0.4213 b. 0.3571 c. 0.7812 d. 0.4587 e. 0.2743 2. what is the probability that he/she plays exactly one of these types of instruments? a. 0.7821 b. 0.2457 c. 0.5057 d. 0.7571 e. 0.3645 3. what is the probability that he/she plays at most one of these instruments? a. 0.7514 b. 0.9245 c. 0.5151 d. 0.2486 e. 0.8657

The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is calculated by dividing the likelihood of the previous event by the likelihood of the subsequent, or contingent, event.

Here,

Finding people who can play the clarinet but not the flute is necessary. There are 172 people who can play the clarinet.

There are 47 people who can play both the clarinet and the flute.

As a result, 172-47=125 represents the number of people who can only play the clarinet and not the flute.

Probability(P),

P=( 125 / 350)

P=0.2743.

Therefore, the probability that a single person chosen at random can play clarinet but not flute is 0.2743.

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