Write each of these answers to 4 significant digits You can

Write each of these answers to 4 significant digits. You can use Scientific Notation for the Answer.

For example: your decimal answer is 0.0000230567, multiply by 100 to get percent....0.00230567. The four significant digits are 2305, thus for normal answer: 0.002305%, and for Scientific: 2.305E-3%.

(1) The probability of winning a game is 21.5% for each attempt.

(2) What is the probability that you will not win the game (one attempt)?

(3) What is the probability that you will win the game 3 times in a row?

(4) What is the probability of loosing at least once out of 3 times of playing this game?

(5) What is the probability of loosing 3 in a row?

(6) What is the probability of winning at least once when the game is played 3 times in a row?

What is the probability of winning at least once when the game is played 3 times in a row?

Solution

(1) Probability of winning the game = 21.5 % = 0.215

If we want to answer in four significant digits then the answer would be 0.2150

In terms of scientific notations, the answer will be 2.150 * 10^{-1}

(2) Probability of not winning the game = 1 - Probability of winning the game = 1 - 21.5 % = 78.5% = 0.785

If we want to answer in four significant digits then the answer would be 0.7850

In terms of scientific notations, the answer will be 7.850 * 10^{-1}

(3) Probability of winning three games in a row

=> p^3 = (0.215)^3 = 0.009938375

If we want to answer in four significant digits then the answer would be 0.009938

In terms of scientific notations, the answer will be 9.938 * 10^{-3}

(4) Probability of lossing at least one game

=> 1 - P(winning all the games)

=> 1 - 0.009938375

=> 0.990061625

If we want to answer in four significant digits then the answer would be 0.9901

In terms of scientific notations, the answer will be 9.901 * 10^{-1}

(5) Probability of winning three games in a row

=> (1-p)^3 = (1 - 0.215)^3 = 0.483736225

If we want to answer in four significant digits then the answer would be 0.4837

In terms of scientific notations, the answer will be 4.837 * 10^{-1}

(6) Probability of winning at least one game

=> 1 - P(losing all the games)

=> 1 - 0.483736225

=> 0.516263775

If we want to answer in four significant digits then the answer would be 0.5163

In terms of scientific notations, the answer will be 5.163* 10^{-1}