# Binomial distribution and probability of observing an event.

Jared bets on the number 7 for each of 100 spins of a roulette wheel. Because P(7) = 1/38 he expects to win two or three times. What is the probability that Jared will actually win two or more times?

This was a quiz question I answered incorrectly, I want to understand how to get it if a similar question is on the mid term.

The correct answer was about 3 out of 4.

Can you please explain how this was determined.

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:42 pm ad1c9bdddfhttps://brainmass.com/statistics/probability/binomial-distribution-probability-observing-event-210934

## SOLUTION This solution is **FREE** courtesy of BrainMass!

To answer this problem, you need to use the binomial distribution formula (see Excel file).

The formula gives us the probability that something occurs k times. So if we use k = 1, we get the probability that Jared wins k times. To find the probability that he wins 2 or more times, we have to find the probabilities for k = 2, k = 3, k = 4, ..., up to k = 100, then add them up. Luckily for us, the probabilities get close to 0 as k increases, so if we only need an estimate, we can just add up the first few probabilities.

Probability that k is 2 or more = 0.742695276

This is close to 75%, or 3 out of 4.

Â© BrainMass Inc. brainmass.com December 24, 2021, 7:42 pm ad1c9bdddf>https://brainmass.com/statistics/probability/binomial-distribution-probability-observing-event-210934