[tex] \displaystyle
|\Omega|=\binom{8}{3}=\dfrac{8!}{3!5!}=\dfrac{6\cdot7\cdot8}{2\cdot3}=56\\
|A|=5\cdot\binom{3}{2}=5\cdot3=15\\\\
P(A)=\dfrac{15}{56}\approx27\% [/tex]
The probability that the spider - man eats exactly one chocolate with coconut is 0.268.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1.
Given -
Total number of chocolates = 8
Number of chocolates with coconut = 5
Number of chocolates without coconut = Number of chocolates with pecans or raspberry = 2 + 1 = 3
Number of ways of choosing 3 chocolates out of 8 = [tex]{8}_C_{3}[/tex] = 56
Number of ways of choosing 1 chocolate out of 3 coconut chocolates and 2 chocolates out of 5 non coconut chocolates = [tex]{3}_C_{1} * {5}_C_{2}[/tex] = 3 x 5 = 15
Probability that spider man will eat exactly one chocolate with coconut =
= [tex]\frac{Favourable\ number\ of outcomes}{Total\ number\ of\ outcomes}[/tex] = [tex]\frac{15}{56}[/tex] = 0.268
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