There are 20 black cell phones and 30 white cell phones in a store. An employee takes 10 phones at random. Find the probability that there will be exactly 4 black cell phones among the chosen phones; there will be less than 3 black cell phones among the chosen phones.
Answers
Given : There are 20 black cell phones and 30 white cell phones in a store. An employee takes 10 phones at random.
To Find : the probability that there will be exactly 4 black cell phones among the chosen phones;
there will be less than 3 black cell phones among the chosen phones.
Solution:
Black = 20
White = 30
Total = 50
10 out of 50 can be selected in ⁵⁰C₁₀ ways
exactly 4 black cell phones means
Black = 4 and white = 6
=> ways = ²⁰C₄ * ³⁰C₆
probability that there will be exactly 4 black cell phones
= ²⁰C₄ * ³⁰C₆ / ⁵⁰C₁₀
less than 3 black cell phones
= Black 2 White 8 or Black 1 White 9 or Black = 0 White 10
Ways = ²⁰C₂ * ³⁰C₈ + ²⁰C₁ * ³⁰C₉ + ²⁰C₀* ³⁰C₁₀
Probability = ( ²⁰C₂ * ³⁰C₈ + ²⁰C₁ * ³⁰C₉ + ²⁰C₀* ³⁰C₁₀ ) / ⁵⁰C₁₀
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