MATHEMATICS MIDDLE SCHOOL

Someone rolls a six sided fair die 5 times. They consider it a success if they have a two or three on a die. Whats the probability of 2 successes? no successes? and at least 3 successes?

Answers

Answer 1
Answer:

Answer:

2 successes =  80/243

0 successes = 32/243

at least 3 successes = 51/243

Step-by-step explanation:

Lets suppose we had the following sequence of 5 throws:-

2 or 3,  2 or 3 ,  then NOT 2 or 3 on last 3 throws

Probability of this is

1/3 * 1/3 * 2/3 * 2/3 * 2/3 = 8/243

There are  (5*4) / 2 = 10 ways of having this result  ( that is the number of combinations of 2 from  5   =  5C2 ).

So Prob(2 successes) = (8/243) * 10  = 80/243

Prob ( No successes) =  (2/3)^5 = 32/243

Probability of 3 successes = 1/3 * 1/3 * 1/3 * 2/3 * 2/3 *   5C3  

4/243 * 10 = 40 / 243

Probability of 4 successes =  (1/3)^4 * 2/3 * 5C4

= 10/243

Probability of 5 success = (1/3)^5 = 1 / 243

Prob(at least 3 successes) = 51/243
Answer 2
Answer:

Answer:

2 successes =  80/243

0 successes = 32/243

at least 3 successes = 51/243

Step-by-step explanation:

Lets suppose we had the following sequence of 5 throws:-

2 or 3,  2 or 3 ,  then NOT 2 or 3 on last 3 throws

Probability of this is

1/3 * 1/3 * 2/3 * 2/3 * 2/3 = 8/243

There are  (5*4) / 2 = 10 ways of having this result  ( that is the number of combinations of 2 from  5   =  5C2 ).

So Prob(2 successes) = (8/243) * 10  = 80/243

Prob ( No successes) =  (2/3)^5 = 32/243

Probability of 3 successes = 1/3 * 1/3 * 1/3 * 2/3 * 2/3 *   5C3  

4/243 * 10 = 40 / 243

Probability of 4 successes =  (1/3)^4 * 2/3 * 5C4

= 10/243

Probability of 5 success = (1/3)^5 = 1 / 243

Prob(at least 3 successes) = 51/243

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Answers

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Answers

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Step-by-step explanation:

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a wooden board is 100 centimeters long is cut into two pieces one is 16 centimeters longer than the other what are the lengths of the two pieces

Answers

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Problema Solution a wooden board 100 centimeters long is cut into two pieces. One piece is 16 inches longer than the other. What are the lengths of the two pieces x = the length of one piece y = the length of the other piece the total length is 100 cm this means x + y = 100 one piece is 16 inches longer than the other first we need to convert inches to cm: 1 in = 2.54 cm 16 in = 2.54*16 = 40.64 now we can write x = y + 40.64 by solving the system of equations x + y = 100 x = y + 40.64 we find x = 70.32 cm y = 29.68 cm the lengths of the two pieces are 70.32 cm and 29.68 cm.

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Answers

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Answers

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Answers

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