Mary Beth R. answered • 06/21/23
MS in Mathematics with Data Science credentials
Are you aware that "n" represents the "number of trials" or attempts at success?
Think... basketball. Any time you attempt a foul shot, the likelihood of you succeeding is 0.6... which means that, on average you make the extra point 6 out of 10 times that you try. On average is the key.
In this situation, we only get 6 shots. We are asked to find the probability that the "number of shots made" is less than 6. Given our 0.6 rating, we expect this probability to be pretty high... that is, it will be a decimal very close to "1"... at least 0.9 I expect.
P(x < 6) after all is P(x=1) + P(x=2) + P(x=3) + P(x=4) + P(x=5). Do you want to calculate all of those probabilities? No? Me neither.
Instead, since we know that ALL of the probabilities must add up to 1, we can do this:
1 - P(x=6). We only need to calculate one probability, and subtract it from 1.
P(x=6) when number of trials = 6, number of successes (k) = 6, and p = 0.6.
[There is a nice tool that calculates binomial probabilities on statology.org Look up "binomial distribution calculator" and enter the 3 values there.] Voila!
Does this help?
