Using the principle of binomial probability, the probability that more than 3 friends win a prize is
Recall :
- P(x = x) = nCx * p^x * q^(n-x)
<u>Given</u><u> </u><u>the</u><u> </u><u>Parameters</u><u> </u><u>:</u>
- <em>Probability</em><em> </em><em>of</em><em> </em><em>success</em><em>,</em><em> </em><em>p</em><em> </em><em>=</em><em> </em><em>1</em><em>/</em><em>6</em><em> </em>
- <em>q</em><em> </em><em>=</em><em> </em><em>1</em><em> </em><em>-</em><em> </em><em>p</em><em> </em><em>=</em><em> </em><em>5</em><em>/</em><em>6</em><em> </em>
- <em>Number</em><em> </em><em>of</em><em> </em><em>trials</em><em>,</em><em> </em><em>n</em><em> </em><em>=</em><em> </em><em>7</em>
- <em>x</em><em>≥</em><em>3</em><em> </em>
Hence,
P(x ≥ 3) = p(x = 3) + p(x = 4) + p(x = 5) + p(x = 6) + p(x = 7)
P(x ≥ 3) = 0.0781 + 0.0156 + 0.0019 + 0.0001 + 0.000003
P(x ≥ 3) = 0.095703
Therefore, the probability that more than 3 friends win a prize is 0.0957
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