I need help in hypergemetric distrubtion Note: please clear your answer and solv

Question

I need help in hypergemetric distrubtion
Note:
please clear your answer and solve step by step and solve by your hend

y Distributions 4.26 Suppose that you are trying to send three different FAX messages to a particular FAX machine. Unknown to you, someone else is sending seven dif. ferent messages to the same FAX machine. A short time after all these messages have been sent, the receiving FAX machine displays the message "seven messages received." If the messages that are lost are n independent of the sender, what is the probability that (a) none of your messages was lost? (b) exactly one of your messages was lost? (c) all three of your messages were lost?

Explanation / Answer

In total there are 10 messages of which only 7 have been sent. This is possible in 10C7 ways

= (10!)/(7!)(3!)

= (10 x 9 x 8)/(6)

= 120.

Thus, the denominator for all the probability calculations would be 120…………… (1)

Part (a)

None of the 3 messages is lost => all 3 of 3 and only 4 of 7 are sent. This is possible in

(3C3) x (7C4) ways

= 1 x 35

= 35.

Hence, the required probability = 35/120 = 0.292 ANSWER

Part (b)

Exactly one the 3 messages is lost => only 2 of 3 and 5 of 7 are sent. This is possible in

(3C2) x (7C5) ways

= 3 x 21

= 63.

Hence, the required probability = 63/120 = 0.525 ANSWER

Part (c)

All the 3 messages are lost => none of 3 and all 7 of 7 are sent. This is possible in

(3C0) x (7C7) ways

= 1 x 1

= 1.

Hence, the required probability = 1/120 = 0.0083 ANSWER

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