ProbabilityHardBloom L3
Question
Each packet of blades sold contains a coupon which is equally likely to bear the letters A, B or C. If 'm' packets are purchased, what is the probability that the coupons can not be to used to spell BAC .
Options
A.$\left( \frac{2}{3} \right)^{m}$
B.$\frac{{3.2}^{m} - 2}{3^{m}}$
C.$\frac{2^{m}}{3^{m - 1}}$
D.$\frac{2^{m} - 1}{3^{m - 1}}$
Solution
Sol. [Key Concept: Coupons can't spell BAC: inclusion–exclusion gives $\frac{3 \cdot 2^{m} - 3}{3^{m}}$.]
$$P = \frac{\ ^{3}C_{1}2^{m} - \ ^{3}C_{2}(1)^{m}}{3^{m}} = \frac{2^{m} - 1}{3^{m - 1}} $$$A \rightarrow$ number of ways s.t. there is no A
$B \rightarrow$ number of ways s.t. there is no B
$C \rightarrow$ number of ways s.t. there is no C
$$n(A \cup B \cup C) = S_{1} - S_{2} + S_{3} = \ ^{3}C_{1}2^{m} - \ ^{3}C_{2}1^{m} + 0$$
Create a free account to view solution
View Solution FreeMore Probability Questions
Three numbers are selected one by one at random without replacement from the set of numbers $\{ 1,2,3,\ldots\ldots,n\}$....If one card is drawn from a pack of card then the odds in favour of getting Ace is-...A letter is known to have arrived by post either from KANPUR or from ANANTPUR. On the the envelope just two consecutive ...A determinant is chosen at random from the set of all determinant of order 2 with elements 0 or 1 only. The probability ...The probabilities of events, A ∩ B, A, B & A ∪ B are respectively in A. P. with probability of second term e...