a and b are vectors such that |a| = √3, |b| = 1, and the angle between them is 5π/6. Using scalar product, find the exact value
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Answer:
the probability that their minimum is larger than 5 is 0.2373
Step-by-step explanation:
For calculate the probability we need to make a división between the total ways to selected the 5 numbers and the ways to select the five numbers in which every number is larger than 5.
So the number of possibilities to select 5 numbers from 20 is:
<u>20 </u> * <u> 20 </u>* <u> 20 </u> *<u> 20 </u>* <u> 20 </u>
First number 2nd number 3rd number 4th number 5th number
Taking into account that a number can be chosen more than once, and the order in which you select the numbers matters, for every position we have 20 options so, there are ways to select 5 numbers.
Then the number of possibilities in which their minimum number is larger than 5 is calculate as:
<u>15 </u> * <u> 15 </u>* <u> 15 </u> *<u> 15 </u>* <u> 15 </u>
First number 2nd number 3rd number 4th number 5th number
This time for every option we can choose number from 6 to 20, so we have 15 numbers for every option and the total ways that satisfy the condition are
So the probability P can be calculate as:
Then the probability that their minimum is larger than 5 is 0.2373