Probability Question 7
Question 7 - 29 January - Shift 1
Fifteen football players of a club-team are given 15 T-shirts with their names written on the backside. If the players pick up the T-shirts randomly, then the probability that at least 3 players pick the correct T-shirt is
(1) $\frac{5}{24}$
(2) $\frac{2}{15}$
(3) $\frac{1}{6}$
(4) $\frac{5}{36}$
Show Answer
Answer: (3)
Solution:
Formula: Probability of occurrence of an event
Required probability $ = 1-\frac{D _{(15)}+{ }^{15} C_1 \cdot D _{(14)}+{ }^{15} C_2 D _{(13)}}{15 !}$
Taking $D _{(15)}$ as $\frac{15 !}{e} \quad D _{(14)}$ as $\frac{14 !}{e} \quad D _{(13)}$ as $\frac{13 !}{e}$
$ \begin{aligned} & \text{ We get, } 1-(\frac{\frac{15 !}{e}+15 \cdot \frac{14 !}{e}+\frac{15 \times 14}{2} \times \frac{13 !}{e}}{15 !}) \\ & =1-(\frac{1}{e}+\frac{1}{e}+\frac{1}{2 e})=1-\frac{5}{2 e} \approx .08 \end{aligned} $
