Solving Probability Problem: 11/20 x 9/19 = 266/380

  • Thread starter Gringo123
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So the probability that they have different hair colours is 11/20 x 18/19 + 7/20 x 13/19 + 2/20 x 9/19 = 198/380 + 91/380 + 18/380 = 307/380.In summary, the probability that two students chosen at random from a class of 20 have different hair colours is 307/380. The correct answer is 266/380, which can be obtained by calculating the probability of the complementary event (the two students having the same hair color) and subtracting it from 1. Your calculation of 99/380 is incorrect because it does not account for the possibility of the second student having
  • #1
Gringo123
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Can anyone help me with this?

In a class of 20 pupils, 11 have dark hair, 7 have blond hair and 2 have red hair. 2 Pupils are chosen at random to collect the homework. What is the probability that each have a different colour hair?

The correct answer is 266/380

However I thought it would be 99/380. I arrived at that answer in the following way:

11/20 x 9/19 = 99/380

Where did I go wrong?
 
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  • #2
In your setup you don't ensure the second person has hair of a different color than the first.
 
  • #3
Hi. Thanks for your reply but I'm afraid I don't understand. Would you mind laying it out for me as it should be done?
Thanks again for your help.
 
  • #4
Well, I assume you are aware on how to calculate the probability of the complementary event?

In short, try to calculate the probability that the 2 chosen pupils have the same hair colour, which should be easier to deal with.
 
  • #5
The probability that the first student has black hair is 11/20 and the probability that the second student does NOT is 9/19 (because there are now 19 students left and the first had black hair so all blond and redheaded students are still left.

The probability that the first student has blonde hair is 7/20 and the probability that the second student does NOT is 13/19.

The probability that the first student has red hair is 2/20 and the probability that the second student does NOT is 18/19.

The probability that "A and B" happen is the product of probabilities of A and B separately and the probability that one of three different things happen is their sum.
 

FAQ: Solving Probability Problem: 11/20 x 9/19 = 266/380

What is the formula for solving a probability problem?

The formula for solving a probability problem is to divide the number of desired outcomes by the total number of possible outcomes.

How do you solve for probability when given fractions?

To solve for probability when given fractions, you must first multiply the fractions together. In this case, you would multiply 11/20 by 9/19, which equals 99/380. Then, you can simplify the fraction by dividing the numerator and denominator by the greatest common factor. In this example, the greatest common factor is 19, so the final answer is 11/20 x 9/19 = 266/380.

What is the difference between probability and odds?

Probability is the likelihood or chance of an event occurring. It is expressed as a decimal or fraction between 0 and 1. Odds, on the other hand, are the ratio of the number of desired outcomes to the number of undesired outcomes. Odds can be expressed as a fraction, decimal, or ratio.

How do you know if your probability answer is correct?

To ensure your probability answer is correct, you can check that it falls between 0 and 1, as probabilities cannot be negative or greater than 1. Additionally, you can use the formula for probability to calculate the answer again and compare it to your original answer.

Can probability be greater than 1?

No, probability cannot be greater than 1. A probability of 1 means that the event is certain to occur, while a probability of 0 means that the event is impossible. A probability between 0 and 1 represents the likelihood or chance of an event occurring.

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