Answer:
0.15
Step-by-step explanation:
Without Mincing words let us dive straight into the solution to the question above. We are given the following information which is going to aid in solving this particular question.
====> It is given, that there are 5 white balls and 10 red balls. Hence, the number of the total balls = 5 white balls + 10 red balls = 15 balls.
Therefore, the probability that 5 randomly selected balls contain exactly 3 white balls = [tex]\left[\begin{array}{ccc}5\\3\end{array}\right][/tex] × [tex]\left[\begin{array}{ccc}10\\2&\end{array}\right][/tex] ÷ [tex]\left[\begin{array}{ccc}15\\3\\\end{array}\right][/tex] = 450 ÷ 3003 = 0.15
Given:
The number of chosen 5 balls out of 15 will be:
= [tex]\binom{15}{5}[/tex]
= [tex]3003[/tex]
The number of ways 3 white balls chosen from 5 as well as 2 red balls chosen from 10 will be:
= [tex]\binom{5}{3}\times \binom{10}{2}[/tex]
= [tex]450[/tex]
hence,
The probability that 5 random balls selected will be:
= [tex]\frac{No. \ of \ ways \ the \ event \ can \ happen}{Total \ no. \ of \ ways}[/tex]
By substituting the values, we get
= [tex]\frac{450}{3003}[/tex]
= [tex]0.1499[/tex]
Thus response above is correct.
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