Intermediate Algebra Unit 11 Test Probability & Statistics questions

Question

1) When Sophia’s mom picks her up from school, she is late one third of the time. For the next 15 days, what is the probability that she will be late at most three days?

2) When Tom plays darts, he hits the target 65% of the time. Find the probability that he hits the target at least four out of next six attempts.

3) What is the fourth term in the binomial expansion of (2x – y) 7 ?

Answer 1

The general formula for a given probability (P) happening k times in n trials is

C^k_n P^k(1-P)^(n-k)

This is what you need to use for problems 1 and 2

1) Add the individual probability of 0, 1, 2, and 3 late days out of 15

P(0 days) = (2/3)¹⁵ Notice that I have made P the probability of NOT being late.

P(1 day) = 15(2/3)¹⁴(1/3)

P(2 days) = 105(2/3)¹³(1/3)²

P(3 days) = 455(2/3)¹²(1/3)³

Add these up and that's the answer to question (1) Note 455 is 15!/(3!12!)

2) I'll leave for you

3) The kth term of the binomial (a+b)ⁿ is C^k_n a^k b^(n-k) You should be able to do this by just substituting the values given.

Good luck! Hope that helps.