Consider the binomial expansion for 6 events: P ₆ + 6 P ₅ Q + 15 P ₄ Q ₂ + 20 P ₃ Q ₃ + 15 P ₂ Q ₄ + 6 PQ ₅ + Q ₆ What term(s) would you use to evaluate the probability of obtaining 1 or fewer heads from 6 flips of an unbiased coin? A) 6 PQ ₅ B) 6 PQ ₅ + Q ₆ C) Q ₆ D) 20 P ₃ Q ₃

Question

Quizplus · Accepted Answer

We need to find the probability of obtaining 1 or fewer heads in 6 flips. This is equivalent to the probability of getting 5 or 6 tails. From the given binomial expansion, the terms that represent 5 tails and 6 tails are: 6 PQ ₅ + Q ₆ Adding these two terms, we get: 6 PQ ₅ + Q ₆ = 6*(1/2)^5*(1/2)^1 + (1/2)^6 = 6/64 + 1/64 = 7/64 Thus, the probability of getting 1 or fewer heads is 7/64, which is represented by option B.

Consider the Binomial Expansion for 6 Events: P 6

Consider the Binomial Expansion for 6 Events: P ₆