Question

In: Statistics and Probability

Suppose Emerson loses 30% of all staring contests. (a) What is the probability that Emerson loses...

Suppose Emerson loses 30% of all staring contests.

(a) What is the probability that

Emerson loses two staring contests in a row?

(b) What is the probability that

Emerson loses three staring contests in a row?

(c) When events are independent, their complements are independent as well. Use this result to determine the probability that

Emerson loses three staring contests in a row, but does not lose four in a row.

Solutions

Expert Solution

(a)

Probability that Emerson loses staring contests = 0.3

Probability that Emerson loses two staring contests in a row = Probability that Emerson loses in first staring contest * Probability that Emerson loses in second staring contest

= 0.3 * 0.3 = 0.09

(b)

Probability that Emerson loses three staring contests in a row = Probability that Emerson loses in first staring contest * Probability that Emerson loses in second staring contest * Probability that Emerson loses in third staring contest

= 0.3 * 0.3 * 0.3 = 0.027

(c)

Probability that Emerson loses three staring contests in a row = Probability that Emerson loses in first staring contest * Probability that Emerson loses in second staring contest * Probability that Emerson loses in third staring contest * Probability that Emerson wins in fourth staring contest

+

Probability that Emerson wins in first staring contest * Probability that Emerson loses in second staring contest * Probability that Emerson loses in third staring contest * Probability that Emerson loses in fourth staring contest

= 0.3 * 0.3 * 0.3 * (1 - 0.3) + (1 - 0.3) * 0.3 * 0.3 * 0.3

= 0.0189 + 0.0189

= 0.0378


Related Solutions

​Suppose Emerson wins 37% of all bingo games
Suppose Emerson wins 37% of all bingo games  (a) What is the probability that Emerson wins two bingo games in a row?  (b) What is the probability that Emerson wins three bingo games in a row? (c) When events are independent, their complements are independent as well. Use this result to determine the probability that Emerson wins three bingo games in a row, but does not win four in a row.  (a) The probability that Emerson wins two bingo games...
On each bet, a gambler loses $2 with probability 0.2, loses $1 with probability 0.7, or...
On each bet, a gambler loses $2 with probability 0.2, loses $1 with probability 0.7, or wins $10 with probability 0.1. After 100 of these bets, what is the approximate probability that the gambler's total is negative? Show your work below.
Suppose Ari loses 31 ​% of all ping dash pong games . ​(a) What is the...
Suppose Ari loses 31 ​% of all ping dash pong games . ​(a) What is the probability that Ari loses two ping dash pong games in a​ row? ​(b) What is the probability that Ari loses six ping dash pong games in a​ row? ​(c) When events are​ independent, their complements are independent as well. Use this result to determine the probability that Ari loses six ping dash pong games in a​ row, but does not lose seven in a...
Suppose that jurors are selected randomly from an adult population. What is the probability that all...
Suppose that jurors are selected randomly from an adult population. What is the probability that all 12 jurors are white when 67% of the population is white? Round you answer to three decimal places.
In your opinion, is Emerson wise to reposition itself by branding all of its divisions with...
In your opinion, is Emerson wise to reposition itself by branding all of its divisions with the Emerson name? Why would this be beneficial in selling to business markets? How might it be a disadvantage?
The ball in Task 1 will then continue to bounce and rebound until it loses all energy.
  Task 2 – Subsequent Motion The ball in Task 1 will then continue to bounce and rebound until it loses all energy. By first finding an expression for the maximum height of the ball after the first bounce, find formulas for the total distance travelled by the ball (i.e. the total distance travelled up and down for all bounces) and the total time taken to complete its motion. A ball of mass 0.06 kg is dropped from rest from...
If Huawei loses their case and the US is able to ban all government projects from...
If Huawei loses their case and the US is able to ban all government projects from ecer purchasing Huawei products, how might this affect US public policy going forward?
What is the probability that a class of 30 students out of 300 would have a...
What is the probability that a class of 30 students out of 300 would have a final average grade higher than a 90? 95   96   94   58   67   94   89   88   97   76 50   94   61   63   78   90   79   81   98   64 86   91   92   95   85   79   89   88   95   92 94   65   40   80   93   81   95   89   91   88 96   58   88   77   98   91   97   79   93   94 92   91   61   74   90   89   80  ...
Suppose the probability of a part being manufactured by Machine A is 0.6 Suppose the probability...
Suppose the probability of a part being manufactured by Machine A is 0.6 Suppose the probability that a part was manufactured by Machine A and the part is defective is 0.09 Suppose the probability that a part was NOT manufactured by Machine A and the part IS defective is 0.13 Find the probability that Machine A produced a specific part, given that the part was defective. Round your final answer to 2 decimals, if needed.
Suppose the probability that the probability of rain today in Vernon is 0.4 and the probability...
Suppose the probability that the probability of rain today in Vernon is 0.4 and the probability of rain today in Kelowna is 0.3. The probability that it will rain in both cities today is 0.2. A) What is the probability that it will rain in Kelowna or Vernon today? B) What is the probability that it will rain Kelowna today but not in Vernon? C) Suppose that it has started to rain in Kelowna today. What is the conditional probability...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT