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Binomial Probability 'At Most' and 'At Least' MathBitsNotebook.com Topical Outline Algebra 2 Outline MathBits' Teacher Resources Terms of Use Contact Person:Donna Roberts |
When computing 'at least' and 'at most' probabilities, it is necessary to consider, in addition to the given probability, • all probabilities larger than the given probability ('at least') • all probabilities smaller than the given probability ('at most') |
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Illustration:
A bag contains 6 red Bingo chips, 4 blue Bingo chips, and 7 white Bingo chips. What is the probability of drawing a red Bingo chip at least 3 out of 5 times? Round answer to the nearest hundredth.
To solve this problem, we need to find the probabilities that r could be 3 or 4 or 5,
to satisfy the condition 'at least'.
It will be necessary to compute
for r = 3, r = 4 and r = 5 (which means do the formula three times)
and add these three probabilities for the final answer.
Written in summation notation, we need to compute:
| For r = 3: | |
| For r = 4: | |
| For r = 5: | |
| Sum: | 0.184 + 0.050 + 0.005 = 0.239 rounded to the nearest hundredth = 0.24 ANS |
Note: it may be helpful to remember in this problem that
'at most 2 successes' is the compliment of 'at least 3 successes'.
In the following examples, answers will be rounded to the nearest hundredth.
A family consists of 3 children. What is the probability that at most 2 of the children are boys? Solution: | |||||
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| Team A and Team B are playing in a league. They will play each other five times. If the probability that team A wins a game is 1/3, what is the probability that team A will win at least three of the five games? | |||||
Solution: 'At least' 3 wins implies 3, 4, or 5 wins.
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| As shown in the accompanying diagram, a circular target with a radius of 9 inches has a bull's-eye that has a radius of 3 inches. If five arrows randomly hit the target, what is the probability that at least four hit the bull's-eye? Express answer to the nearest thousandth. | |||||
Solution: 'At least' 4 hits implies 4 or 5 hits. The area of the bull's-eye is 9π and the area of the entire target is 81π. The probability of hitting the desired bull's-eye is 1/9.
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NOTE: There-posting of materials(in part or whole) from this site to the Internet is copyright violation and is not considered 'fair use' for educators. Please read the 'Terms of Use'. |
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Topical Outline Algebra 2 Outline MathBitsNotebook.com MathBits' Teacher Resources
Terms of Use Contact Person: Donna Roberts
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