Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Find the probability of x successes in n trials for the given probability of success p on each trial.

8. x = 3 , n = 8 , p = 0.3 x equals 3 comma n equals 8 comma p equals 0.3
9. x = 4 , n = 8 , p = 0.3 x equals 4 comma n equals 8 comma p equals 0.3
10. x = 5 , n = 10 , p = 0.5 x equals 5 comma n equals 10 comma p equals 0.5
11. x = 5 , n = 10 , p = 0.1 x equals 5 comma n equals 10 comma p equals 0.1
12. Battery Life A calculator contains four batteries. With normal use, each battery has a 90% chance of lasting for one year. What is the probability that all four batteries will last a year?

See Problem 2.

Expand each binomial.

13. ( a + b ) 4 open eh plus b close to the fourth
14. ( m + 5 n ) 3 open m plus 5 n close cubed
15. ( 3 x + 2 y ) 5 open 3 x plus 2 y close to the fifth
16. ( 4 c − d ) 4 open 4 c minus d close to the fourth

Find the indicated term of each binomial expansion.

17. second term of ( 2 g + 2 h ) 7 open 2 g plus 2 h close to the seventh
18. fifth term of ( x − y ) 5 open x minus y close to the fifth
19. first term of ( e + 3 f ) 6 open e plus 3 f close to the sixth
20. eighth term of ( 3 x − y ) 8 open 3 x minus y close to the eighth

See Problem 3.

Use the binomial expansion of ( p + q ) n open p plus q close to the n  to calculate each binomial distribution.

21. n = 6 , p = 0.3 n equals 6 comma p equals 0.3
22. n = 6 , p = 0.5 n equals 6 comma p equals 0.5
23. n = 6 , p = 0.9 n equals 6 comma p equals 0.9
24. n = 8 , p = 0.45 n equals 8 comma p equals , 0.45

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