First slide

Random variable and probability distribution

Question

A coin whose faces are marked 3 and 5 is tossed 4 times. The probability that the sum of the numbers thrown is greater than 15 is

Moderate

A

$\frac{11}{16}$
B

$\frac{5}{16}$
C

$\frac{5}{8}$
D

$\frac{1}{16}$

Solution

$let ' r' denote the number of times 3 appears n = 4, r = 0, 1, 2, 3, 4$
$^{'} P^{'} be the probability of a coin showing 3$
$\begin{array}{l} \Rightarrow p = \frac{1}{2}, p + q = 1 \\ \Rightarrow q = \frac{1}{2} \end{array}$
Sum is greater than 15
At least 2 coins show 5
At most 2 coins show 3
$P (0 \leq X = r \leq 2)$
$= P (X = 0) + P (X = 1) + P (X = 2) (∵ P (X = r) = n_{C_{r}} p^{r} q^{n - r})$
$= 4_{C_{0}} . P^{0} . q^{4} + 4_{{C_{1}}_{}} . p^{1} q^{3} + 4_{C_{2}} . p^{2} q^{2}$
$= {(\frac{1}{2})}^{4} (1 + 4 + 6)$
$= \frac{11}{16}$

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