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# Binomial distribution and probability of observing an event.

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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.

Can you please explain how this was determined.

https://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.

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