Question

A satellite system consists of $n$ components and functions on any given day if at least $k$ of the $n$ components function on that day. On a rainy day, each of the components independently functions with probability $p_{1},$ whereas on a dry day, each independently functions with probability $p_{2} .$ If the probability of rain tomorrow is $\alpha,$ what is the probability that the satellite system will function?

Name: A satellite system consists of n components and functions on any given day if at least k of the n components function on that day. On a rainy day, each of the components independently functions with probability p1, whereas on a dry day, each independently functions with probability p2 . If the probability of rain tomorrow is α, what is the probability that the satellite system will function?
Uploaded: 2021-12-12T20:03:47-08:00
Duration: 4 min 32 s
Channel: Satyam Gupta
Description: A satellite system consists of n components and functions on any given day if at least k of the n components function on that day. On a rainy day, each of the components independently functions with probability p1, whereas on a dry day, each independently functions with probability p2 . If the probability of rain tomorrow is α, what is the probability that the satellite system will function?

          A satellite system consists of $n$ components and functions on any given day if at least $k$ of the $n$ components function on that day. On a rainy day, each of the components independently functions with probability $p_{1},$ whereas on a dry day, each independently functions with probability $p_{2} .$ If the probability of rain tomorrow is $\alpha,$ what is the probability that the satellite system will function?

Added by Zachary A.

Probability with Applications in Engineering, Science, and Technology

Matthew A. Carlton • Jay L. Devore 2nd Edition

Instant Answer

Solved by Expert Satyam Gupta

12/12/2021

Step 1

Step 1: Define the random variables: Let $R$ be the event that it rains tomorrow, $X$ be the random variable representing the number of working components given that it rains, and $Y$ be the random variable representing the number of working components given that Show more…

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A satellite system consists of $n$ components and functions on any given day if at least $k$ of the $n$ components function on that day. On a rainy day, each of the components independently functions with probability $p_{1},$ whereas on a dry day, each independently functions with probability $p_{2} .$ If the probability of rain tomorrow is $\alpha,$ what is the probability that the satellite system will function?