Question

100 plays were made with 5 coins, of which 31 gave 3 faces and 2 crosses. Do this exercise for the combination equation and determine what is the expected number of 3-sided plays and 2 crosses in 100 plays.

Answer 1

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ANSWER::-

AS FOR GIVEN DATA...

100 plays were made with 5 coins, of which 31 gave 3 faces and 2 crosses. Do this exercise for the combination equation and determine what is the expected number of 3-sided plays and 2 crosses in 100 plays.

SOL ::-

total no of outcomes when we toss 5 coins = (no of possible outcomes of each coin)⁵

= 2⁵ = 32

No of outcomes in which 3 faces and 2 crosses occur = (No of ways to select 3 coins from 5)*(No of ways to select 2 coins from remaining 2 coins)

No of ways to select r objects from n objects =

No of ways to select 3 coins from 5 = ⁵C₂ = 5!/(3!*2!) = 10

No of ways to select 2 coins from remaining 2 coins = 1

No of outcomes in which 3 faces and 2 crosses occur = 10*1 = 10

Proability that 3 faces and 2 crosses occur in one play = No of outcomes in which 3 faces and 2 crosses occur/total no of outcomes when we toss 5 coins

=10/32 = 0.3125

expected number of 3-sided plays and 2 crosses in 100 plays = n*Proability that 3 faces and 2 crosses occur in one play = 100*0.3125 = 31.25 ~ 31

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