SOLUTION: Hi Could you please help me to solve this problem:
Find a probability if a die is rolled 5 times: P(exactly one 5)
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Probability-and-statistics
-> SOLUTION: Hi Could you please help me to solve this problem:
Find a probability if a die is rolled 5 times: P(exactly one 5)
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You can put this solution on YOUR website! A DIE HAS 6 FACES.WHEN IT IS ROLLED ANY FACE CAN TURN UP.SO IN ONE THROW WE CAN GET 5 ONLY IN ONE OUT OF 6 CHANCES OR PROBABILITY OF 1/6.
FOR NOT GETTING A 5 ,THE PROBABILITY =5/6 ...WE SAY PROBABILITY OF SUCCESS=P=1/6
SINCE THAT IS WHAT WE WANT.
PROBABILITY OF FAILURE =Q=5/6
NOW WE USE BINOMIAL DISTRIBUTION THEOREM TO FIND PROBABILITY IN MANY TROWS OR 5 THROWS AS REQUIRED HERE.IT SAYS
PROBABILITY OF EXACTLY R SUCCESSES IN N TRIALS =(NCR)*(P^R)*(Q^(N-R))
WE HAVE N=5 AND R=1,P=1/6...Q=5/6
P(1)=5C1*((1/6)^1)*((5/6)^4)=(5*5*5*5*5)/(6*6*6*6*6)=0.4019
