In a group of 16 pupils, 1 plays the flute only. 1 plays the piano only. 11 play both instruments. A student is chosen at random
1 answer:
Answer:
3/16
Step-by-step explanation:
16 pupils, 11 play both, 1 plays piano only and 1 flute only
⇒ 11 + 1 + 1 = 13 pupils who play at least one instrument
⇒ 16 - 13 = 3 pupils who don't play either instrument
⇒ Out of the 16 total pupils, 3 play neither, putting this into numbers:
which is then also the answer.
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Using the binomial distribution, it is found that:
The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.
For each question, there are only two possible outcomes, either the guess is correct, or it is not. The guess on a question is independent of any other question, hence, the binomial distribution is used to solve this question.
Binomial probability distribution
The parameters are:
- x is the number of successes.
- n is the number of trials.
- p is the probability of a success on a single trial.
In this problem:
- There are 20 questions, hence
.
- Each question has 2 options, one of which is correct, hence
The probability is:
In which:
Then:
The probability that the student will get 15 correct questions in this test by guessing is 0.0207 = 2.07%.
You can learn more about the binomial distribution at brainly.com/question/24863377