Suppose a 5-bit message is transmitted from a source to a destination through a noisy channel. The probability that a bit of the message gets flipped during transmission is 0.01. Flipping of each bit is independent of one another. The probability that the message is delivered error-free to the destination is ______ . (rounded off to three decimal places)
The problem involves determining the probability that a 5-bit message is transmitted without errors when each bit has a probability of 0.01 of being flipped. Since the flipping of each bit is independent, we can find the probability that each individual bit is not flipped, and then extend this to the whole message.
The probability that a single bit is not flipped is:
P(not flipped) = 1 - P(flipped) = 1 - 0.01 = 0.99
Since the message consists of 5 independent bits, the probability that the entire 5-bit message is error-free (i.e., none of the bits are flipped) is:
P(error-free message) = 0.995
Calculating this gives:
P(error-free message) = 0.995 = 0.9509900499...
Rounding to three decimal places, we get:
P(error-free message) ≈ 0.951
Verifying against the given range (0.949, 0.952), this value indeed falls within the specified range. Thus, the probability that the 5-bit message is delivered error-free is 0.951.
Important Questions from Basics of Probability
- A quadratic polynomial $(x - \alpha)(x - \beta)$ over complex numbers is said to be square invariant if $(x - \alpha)(x - \beta) = (x - \alpha^2)(x - \beta^2)$. Suppose from the set of all square invariant quadratic polynomials we choose one at random.
The probability that the roots of the chosen polynomial are equal is ____________ (rounded off to one decimal place) - If, out of 50 fish of a pond, 12 had no ectoparasite and remaining had varying numbers of parasites on them, then how many of fish had at least one parasite ?
For a distribution with mean, median, mode and standard deviation 25, 24, 26 and 5 respectively, Karl Pearson's coefficient of skewness equals to:
Suppose two distributions have the same mean, same standard deviation and are equally skewed, but the first distribution is more peaked than the
other. This feature of the frequency distributions in which they are different are called:For two equally likely, exhaustive and independent events A and B, P(A ∩ B) is:
